Perhitungan Tulangan Kolom Balok Plat Beton

PERHITUNGA PERHI TUNGAN N PLAT LANTAI SLAB! P)%T )T&' $%T& $%T& %'%( 6 WAY SLAB

A. DATA BAHAN STRUKTUR Kuat tekan beton, Tegangan leleh baja untuk tulangan lentur,

 78 =  y =

20 240

MPa MPa

)x = )y = h=

5.00 1.50 120

m m mm

B. DATA DATA PLA PL AT LANTAI L ANTAI Panjang bentang plat arah x, Panjang bentang plat arah y, Tebal plat lantai, Koei!ien momen plat untuk "

)y * )x =

0 .# 0 KOEFISIEN MOMEN PLA PLAT T $%T& %'%( karena )y*)x+0.4 9lx = )apangan x # 9ly = )apangan y 19tx = Tumpuan x - 9ty = Tumpuan y 5-

∅ = t! =

iameter tulangan yang /igunakan, Tebal ber!ih !elimut beton,

10 20

C. BEBAN PLAT LANTAI ". BEBAN MATI  DEAD LOAD!

o 1 2 #

Jenis Beban Mati

;erat !en/iri plat lantai k*m# ;erat finishing lantai lantai k*m# ;erat plaon /an rangka k*m2

Berat satuan

24.0 22.0 0.2

Tebal m 0. 0 .1 2 0. 0 .0 5 

: k*m2 2.330 1.100 0.200

mm mm

4

;erat in!tala!i M k*m2 Total beban mati, %. BEBAN HIDUP  LIVE LOAD!

0.5



: =

;eban hi/up pa/a lantai bangunan =

0.500 4.30

:) =

#00 #.000

kg*m2 k*m2

:u = 1.2 ? : @ 1. ? :) =

10. 41

k*m2

<.#-4 4.421<.-<0 14.34# 1<.-<0

km*m km*m km*m km*m km*m

#. BEBAN RENCANA TERFAKTOR

;eban ren7ana teraktor,

$. MOMEN PLAT AKIBAT BEBAN TERFAKTOR

Momen lapangan arah x, Momen lapangan arah y, Momen tumpuan arah x, Momen tumpuan arah y, Momen ren7ana mak!imum plat,

Mulx = 9lx ? 0.001 ? :u ? )x2 = Muly = 9ly ? 0.001 ? :u ? )x2 = Mutx = 9tx ? 0.001 ? :u ? )x2 = Muty = 9ty ? 0.001 ? :u ? )x2 = Mu =

D. PENULANGAN PLAT

β1 = β1 = 0.35  0.05 ?   78  #0 * - = β1 = aktor bentuk /i!tribu!i tegangan beton,

&ntuk "  78 ≤ #0 MPa, &ntuk "  78 A #0 MPa,

0.35  0.35

'a!io tulangan pa/a kon/i!i balance,

ρb = β1? 0.35 ?  78*  y ? 00 *  00 @  y  =

0.04#0

aktor tahanan momen mak!imum,

'max = 0.-5 ? ρb ?  y ? B 1 C D? 0.-5 ? ρb ?  y *  0.35 ?  78 E = 5.<-3 φ = aktor re/uk!i kekuatan lentur, lentur, 0.30 /! = t! @ ∅ * 2 = >arak tulangan terha/ap !i!i luar beton, 2 5.0 / = h  / ! = Tebal eekti plat lantai, <5 .0 b = 10 itinjau plat lantai !elebar 1 m, 1000 Mn = Mu * φ = Momen nominal ren7ana, 24.-#3  2 'n = Mn ? 10 *  b ? /  = 2.-4105 aktor tahanan momen,

mm mm mm km

'n

+

'max

OK!

'a!io tulangan yang /iperlukan "

ρ = 0.35 ?  78 *  y ? B 1  √ B 1 C 2 ? 'n *  0.35 ?  78  E = 0.0125 ρmin = 0.0025 'a!io tulangan minimum, ρ= 'a!io tulangan yang /igunakan, 0.0125 %! = ρ ∗ b ? / = )ua! tulangan yang /iperlukan, 11<0 2 ! = π * 4 ? ∅ ? b * %! = >arak tulangan yang /iperlukan,  !max = 2 ? h = >arak tulangan mak!imum, 240 !max = >arak tulangan mak!imum, 200 ! =  >arak !engkang !engkang yang yang haru! /igunakan, /igunakan,  ! = 0 iambil jarak !engkang " 0 10 & 0 igunakan tulangan, %! = π * 4 ? ∅2 ? b * ! = )ua! tulangan terpakai, 1#0<

mm2 mm mm mm mm mm mm2

E. KONTROL LENDUTAN PLAT

7 = 4-00?G  78 = Mo/ulu! ela!ti! beton, 2101< MPa ! = 2.00@05 MPa Mo/ulu! ela!ti! baja tulangan, : = : @ :) = ;eban merata tak teraktor pa/aplat, -.30 *mm )x = Panjang bentang plat, 5000 mm )x * 240 = ;ata! len/utan mak!imum yang /iijinkan, 20.3## mm mm # Fg = 1*12 ? b ? h = 144000000 mm# Momen iner!ia brutto penampang plat,  r = 0.- ? G 78 = #.1#04<5135 MPa Mo/ulu! keruntuhan lentur beton, n = ! * 7 = ilai perban/ingan mo/ulu! ela!ti!, < .5 2 7 = n ? %! * b = >arak gari! netral terha/ap terha/ap !i!i ata! beton, beton, 12.455 12.455 mm Momen iner!ia penampang retak yang /itran!orma!ikan ke beton /ihitung !bb. " F7r = 1*# ? b ? 7# @ n ? %! ?  /  7  2 = 355100-< mm4 yt = h * 2 = 0 mm M7r =  r ? Fg * yt = -51#133 mm Momen retak " Momen mak!imum akibat beban tanpa aktor beban " Ma = 1 * 3 ? : ? ) x2 = 24 2400 0000 0000 00 mm mm Fner!ia eekti untuk perhitungan len/utan, Fe =  M7r * Ma # ? Fg @ B 1   M 7r * Ma # E ? F7r = 3-#0443# mm4 )en/utan ela!ti! !eketika akibat beban mati /an beban hi/up "

δe = 5 * #34 ? : ? ) x4 *  7 ? Fe  = ρ = %! *  b ? /  =

#4.05< mm 'a!io tulangan !lab lantai " 0.01#3 aktor ketergantungan Haktu Haktu untuk beban mati jangka Haktu Haktu A 5 tahun, nilai " ζ= 2.0 λ = ζ *  1 @ 50 ? ρ  = 1.1342 )en/utan jangka panjang akibat rangkak /an !u!ut " δg = λ ? 5 * #34 ? : ? )x4 *  7 ? Fe  = 40.##2 mm δtot = δe @ δg = -4.#<0 mm )en/utan total, δtot )x * 240 ≤ $yarat " A 20.3## -4.#<0 BAHA'A NG!

PERHITUNGA PERHI TUNGAN N PLAT LANTAI SLAB! P)%T )T&' &% %'%( TWO WAY SLAB

A. DATA BAHAN STRUKTUR Kuat tekan beton, Tegangan leleh baja untuk tulangan lentur,

 78 =  y =

#5 240

MPa MPa

)x = )y = h=

4.00 5.00 150

m m mm

B. DATA DATA PLA PL AT LANTAI L ANTAI Panjang bentang plat arah x, Panjang bentang plat arah y, Tebal plat lantai, Koei!ien momen plat untuk "

)y * )x =

1 .2 5 KOEFISIEN MOMEN PLA PLAT T &% %'%( karena )y*)x+2 9lx = )apangan x 20 9ly = )apangan y 23 9tx = Tumpuan x 4 9ty = Tumpuan y 5 Tabe( % )en*an $ sisi ter+e,it

∅ = t! =

iameter tulangan yang /igunakan, Tebal ber!ih !elimut beton,

12 20

C. BEBAN PLAT LANTAI ". BEBAN MATI  DEAD LOAD!

o 1 2 #

Jenis Beban Mati

;erat !en/iri plat lantai k*m# ;erat finishing lantai lantai k*m# ;erat plaon /an rangka k*m2

Berat satuan

24.0 22.0 0.2

Tebal m 0. 0 .1 5 0. 0 .0 5 

: k*m2 #.00 1.100 0.200

mm mm

4

;erat in!tala!i M k*m2 Total beban mati, %. BEBAN HIDUP  LIVE LOAD!

0.5



: =

;eban hi/up pa/a lantai bangunan =

:) =

0.500 5.400

#00 #.0

kg*m2 k*m2

11.230

k*m2

#.10 5.05# 11.551 10.1011.551

km*m km*m km*m km*m km*m

#. BEBAN RENCANA TERFAKTOR

;eban ren7ana teraktor,

:u = 1.2 ? : @ 1. ? :) =

$. MOMEN PLAT AKIBAT BEBAN TERFAKTOR

Momen lapangan arah x, Momen lapangan arah y, Momen tumpuan arah x, Momen tumpuan arah y, Momen ren7ana mak!imum plat,

Mulx = 9lx ? 0.001 ? :u ? )x2 = Muly = 9ly ? 0.001 ? :u ? )x2 = Mutx = 9tx ? 0.001 ? :u ? )x2 = Muty = 9ty ? 0.001 ? :u ? )x2 = Mu =

D. PENULANGAN PLAT

β1 =  β1 = 0.35  0.05 ?   78  #0 * - = 0.314235-14# β1 = aktor bentuk /i!tribu!i tegangan beton, 0.314235-14# &ntuk "  78 ≤ #0 MPa, &ntuk "  78 A #0 MPa,


ρb = β1? 0.35 ?  78*  y ? 00 *  00 @  y  =

0.0-21


'max = 0.-5 ? ρb ?  y ? B 1 C D? 0.-5 ? ρb ?  y *  0.35 ?  78 E = 10.14-1 φ = aktor re/uk!i kekuatan lentur, 0.30 /! = t! @ ∅ * 2 = >arak tulangan terha/ap !i!i luar beton, 2.0 / = h  /! = Tebal eekti plat lantai, 124.0 b = 1000 itinjau plat lantai !elebar 1 m, Mn = Mu * φ = Momen nominal ren7ana, 14.4#3  2 'n = Mn ? 10 *  b ? /  = 0.<#<02 aktor tahanan momen,

mm mm mm km

'n

+

'max

OK!


ρ = 0.35 ?  78 *  y ? B 1  √ B 1 C 2 ? 'n *  0.35 ?  78  E = 0.0040 ρmin = 0.0025 'a!io tulangan minimum, ρ= 'a!io tulangan yang /igunakan, 0.0040 %! = ρ ∗ b ? / = )ua! tulangan yang /iperlukan, 4<# 2 ! = π * 4 ? ∅ ? b * %! = >arak tulangan yang /iperlukan, 22< !max = 2 ? h = >arak tulangan mak!imum, #00 !max = >arak tulangan mak!imum, 200 ! = 200 >arak !engkang yang haru! /igunakan, ! = 200 iambil jarak !engkang " 12 & 200 igunakan tulangan, %! = π * 4 ? ∅2 ? b * ! = )ua! tulangan terpakai, 55

mm2 mm mm mm mm mm mm2

E. KONTROL LENDUTAN PLAT Mpa = *mm2 7 = 4-00?G  78 = Mo/ulu! ela!ti! beton, 2-30 MPa ! = 2.10@05 MPa Mo/ulu! ela!ti! baja tulangan, : = : @ :) = ;eban merata tak teraktor pa/aplat, 3.400 *mm )x = Panjang bentang plat, 4000 mm )x * 240 = ;ata! len/utan mak!imum yang /iijinkan, 1.mm # Fg = 1*12 ? b ? h = 231250000 mm# Momen iner!ia brutto penampang plat,  r = 0.- ? G 78 = 4.1412553432 MPa Mo/ulu! keruntuhan lentur beton, n = ! * 7 = ilai perban/ingan mo/ulu! ela!ti!, -.55 7 = n ? %! * b = >arak gari! netral terha/ap !i!i ata! beton, 4.2-1 mm Momen iner!ia penampang retak yang /itran!orma!ikan ke beton /ihitung !bb. " F7r = 1*# ? b ? 7# @ n ? %! ?  /  7  2 = 1243#05 mm4 yt = h * 2 = -5 mm M7r =  r ? Fg * yt = 1552<-0< mm Momen retak " Momen mak!imum akibat beban tanpa aktor beban " Ma = 1 * 3 ? : ? ) x2 = 1300000 mm Fner!ia eekti untuk perhitungan len/utan, Fe =  M7r * Ma # ? Fg @ B 1   M 7r * Ma # E ? F7r = 2#502#55 mm4 )en/utan ela!ti! !eketika akibat beban mati /an beban hi/up "

δe = 5 * #34 ? : ? ) x4 *  7 ? Fe  = ρ = %! *  b ? /  =

4.235 mm 'a!io tulangan !lab lantai " 0.004 aktor ketergantungan Haktu untuk beban mati jangka Haktu A 5 tahun, nilai " ζ= 2.0 λ = ζ *  1 @ 50 ? ρ  = 1.23 )en/utan jangka panjang akibat rangkak /an !u!ut " δg = λ ? 5 * #34 ? : ? )x4 *  7 ? Fe  = .<-3 mm δtot = δe @ δg = 11.2# mm )en/utan total, δtot )x * 240 ≤ $yarat " + 1.11.2# AMAN OK!

PERHITUNGAN BALOK LANTAI BEAM !

A. DATA BALOK LANTAI BAHAN STRUKTUR

Kuat tekan beton, Tegangan leleh baja /eorm untuk tulangan lentur, Tegangan leleh baja polo! untuk tulangan ge!er,

 78 =  y =  y =

2< 400 240

MPa MPa MPa

b= h= = P= t! =

00 50 22 1# -0

mm mm

DIMENSI BALOK

)ebar balok Tinggi balok iameter tulangan /eorm yang /igunakan, iameter !engkang polo! yang /igunakan, Tebal ber!ih !elimut beton,

mm mm mm

MOMEN DAN GA'A GESER RENCANA

Momen ren7ana po!iti akibat beban teraktor, Momen ren7ana negati akibat beban teraktor, Iaya ge!er ren7ana akibat beban teraktor,

Mu@ = Mu  = Ju =

#.1-0 141.##4 1-0.554

km km k

B. PERHITUNGAN TULANGAN

β1 = β1 = 0.35  0.05 ?   78  #0 * - = β1 = aktor bentuk /i!tribu!i tegangan beton, &ntuk "  78 ≤ #0 MPa, &ntuk "  78 A #0 MPa,

0.35  0.35


ρb = β1? 0.35 ?  7L*  y ? 00 *  00 @  y  =

0.0#14


'max = 0.-5 ? ρb ?  y ? B1 C D?0.-5? ρb ?  y *  0.35 ?  7L  E = φ = aktor re/uk!i kekuatan lentur, /! = t! @ ∅ @ *2 = >arak tulangan terha/ap !i!i luar beton, n! =  b  2 ? / ! *  25 @   = >umlah tulangan /lm !atu bari!, n! = igunakan jumlah tulangan /alam !atu bari!,

-.254 0.30 <4.00 3.-3

mm bh

>arak hori!ontal pu!at ke pu!at antara tulangan,

x =  b  n ! ?   2 ? /!  *  n!  1  = ##.-1 y =  @ 25 = 4-.00 >arak ertikal pu!at ke pu!at antara tulangan,

mm mm

". TULANGAN MOMEN POSITIF

Mn = Mu * φ = Momen po!iti nominal ren7ana, -3.<2 /8 = iperkirakan jarak pu!at tulangan lentur ke !i!i beton, -0 / = h  /8 = 530.00 Tinggi eekti balok, 'n = Mn ? 10 *  b ? / 2  = 0.#<12 aktor tahanan momen, @

'n

+

'max

km mm mm

OK!


ρ = 0.35 ?  7L *  y ? B 1  √ ? B1 C 2 ? 'n *  0.35 ?  7L  E = 0.000<< ρmin = √  78 *  4 ?  y  = 'a!io tulangan minimum, 0.00##ρmin = 1.4 *  y = 'a!io tulangan minimum, 0.00#50 ρ = 0.00#50 'a!io tulangan yang /igunakan, %! = ρ ? b ? / = )ua! tulangan yang /iperlukan, 1213 n = %! *  π * 4 ? 2  = >umlah tulangan yang /iperlukan, #.204 4  22 igunakan tulangan, %! = n ? π * 4 ? 2 = )ua! tulangan terpakai, 1521

mm2

mm2

nb = n * n! =

0.50

/8 = Σ B ni ? yi E * n =

<4.00

>umlah bari! tulangan,

nb ;ari! ke 1 2 #

-

#

OK!

>umlah

>arak

>uml. >arak

ni

yi

ni ? yi

4 <4.00 0 0.00 0 0.00 Σ [ ni ? yi E = n= 4 )etak titik berat tulangan, A <4.00 Tinggi eekti balok, Momen nominal, Tahanan momen balok, φ ? Mn $yarat " 20.523

#-.00 0.00 0.00 #- -0

,eriraan (a*i )/ NG!

/ = h  /8 = 55.00 a = %! ?  y *  0.35 ?  78 ? b  = 41.12# Mn = %! ?  y ?  /  a * 2  ? 10  = #25.0 φ ? Mn = 20.523 Mu@ ≥

A

mm

#.1-0

mm mm km km

AMAN OK!

%. TULANGAN MOMEN NEGATIF

Mn = Mu * φ = Momen negati nominal ren7ana, 1-./8 = iperkirakan jarak pu!at tulangan lentur ke !i!i beton, 50 / = h  /8 = 00.00 Tinggi eekti balok, 'n = Mn ? 10 *  b ? / 2  = 0.31-< aktor tahanan momen, 

'n

+

'max

km mm mm

OK!


ρ = 0.35 ?  7L *  y ? B 1  √ ? B1 C 2 ? 'n *  0.35 ?  7L  E = 0.00203 ρmin = √  78 *  4 ?  y  = 'a!io tulangan minimum, 0.00##ρ min = 1.4 *  y = 'a!io tulangan minimum, 0.00#50 ρ = 0.00#50 'a!io tulangan yang /igunakan, %! = ρ ? b ? / = )ua! tulangan yang /iperlukan, 120 2 n = %! *  π * 4 ?   = >umlah tulangan yang /iperlukan, #.#15 4  22 igunakan tulangan, %! = n ? π * 4 ? 2 = )ua! tulangan terpakai, 1521 nb = n * n! = >umlah bari! tulangan, 0.50

mm2

mm2

nb

;ari! ke 1 2 #

-

#

OK!

>umlah

>arak

>uml. >arak

ni

yi

ni ? yi


#-.00 0.00 0.00 #-

/8 = Σ B ni ? yi E * n = 50

<4.00


/ = h  /8 = 55.0 a = %! ?  y *  0.35 ?  78 ? b  = 41.12# Mn = %! ?  y ?  /  a * 2  ? 10  = #25.0 φ ? Mn = 20.523 Mu ≥

A

mm

141.##4

mm mm km km

AMAN OK!

#. TULANGAN GESER

Iaya ge!er ultimit ren7ana, aktor re/uk!i kekuatan ge!er, Tegangan leleh tulangan ge!er, Kuat ge!er beton, Tahanan ge!er beton,

Ju = φ=  y = J7 = G  78 *  ? b ? / ? 10 # = φ ∗ J7 =

1-0.554 0.0 240 #12.#40 13-.404

k MPa k k

Han0a ,er(u tu(.*eser 1in

φ ∗ J! = Ju  φ ∗ J7 = Tahanan ge!er !engkang,  J! = 1-0.554 Kuat ge!er !engkang, 2 P 1# igunakan !engkang berpenampang " % = n! ? π * 4 ? P2 = 25.4 )ua! tulangan ge!er !engkang, ! = % ?  y ? / *  J! ? 10#  = 21. >arak !engkang yang /iperlukan " !max = / * 2 = >arak !engkang mak!imum, 2-3.00 !max = >arak !engkang mak!imum, 250.00 ! = 21. >arak !engkang yang haru! /igunakan,

k k mm2 mm mm mm mm

iambil jarak !engkang " igunakan !engkang,

2

P

1#

! = 210 210

mm

PERHITUNGAN BALOK LANTAI BEAM !

A. DATA BALOK LANTAI BAHAN STRUKTUR

Kuat tekan beton, Tegangan leleh baja /eorm untuk tulangan lentur, Tegangan leleh baja polo! untuk tulangan ge!er,

 78 =  y =  y =

2< 400 240

MPa MPa MPa

b= h= = P= t! =

00 50 22 1# -0

mm mm

DIMENSI BALOK

)ebar balok Tinggi balok iameter tulangan /eorm yang /igunakan, iameter !engkang polo! yang /igunakan, Tebal ber!ih !elimut beton,

mm mm mm

MOMEN DAN GA'A GESER RENCANA

Momen ren7ana po!iti akibat beban teraktor, Momen ren7ana negati akibat beban teraktor, Iaya ge!er ren7ana akibat beban teraktor,

Mu@ = Mu  = Ju =

#.1-0 141.##4 1-0.554

km km k

B. PERHITUNGAN TULANGAN

β1 = β1 = 0.35  0.05 ?   78  #0 * - = β1 = aktor bentuk /i!tribu!i tegangan beton, &ntuk "  78 ≤ #0 MPa, &ntuk "  78 A #0 MPa,

0.35  0.35


ρb = β1? 0.35 ?  7L*  y ? 00 *  00 @  y  =

0.0#14


'max = 0.-5 ? ρb ?  y ? B1 C D?0.-5? ρb ?  y *  0.35 ?  7L  E = φ = aktor re/uk!i kekuatan lentur, /! = t! @ ∅ @ *2 = >arak tulangan terha/ap !i!i luar beton, n! =  b  2 ? / ! *  25 @   = >umlah tulangan /lm !atu bari!, n! = igunakan jumlah tulangan /alam !atu bari!,

-.254 0.30 <4.00 3.-3

mm bh

>arak hori!ontal pu!at ke pu!at antara tulangan,

x =  b  n ! ?   2 ? /!  *  n!  1  = ##.-1 y =  @ 25 = 4-.00 >arak ertikal pu!at ke pu!at antara tulangan,

mm mm

". TULANGAN MOMEN POSITIF

Mn = Mu * φ = Momen po!iti nominal ren7ana, -3.<2 /8 = iperkirakan jarak pu!at tulangan lentur ke !i!i beton, -0 / = h  /8 = 530.00 Tinggi eekti balok, 'n = Mn ? 10 *  b ? / 2  = 0.#<12 aktor tahanan momen, @

'n

+

'max

km mm mm

OK!


ρ = 0.35 ?  7L *  y ? B 1  √ ? B1 C 2 ? 'n *  0.35 ?  7L  E = 0.000<< ρmin = √  78 *  4 ?  y  = 'a!io tulangan minimum, 0.00##ρmin = 1.4 *  y = 'a!io tulangan minimum, 0.00#50 ρ = 0.00#50 'a!io tulangan yang /igunakan, %! = ρ ? b ? / = )ua! tulangan yang /iperlukan, 1213 n = %! *  π * 4 ? 2  = >umlah tulangan yang /iperlukan, #.204 4  22 igunakan tulangan, %! = n ? π * 4 ? 2 = )ua! tulangan terpakai, 1521

mm2

mm2

nb = n * n! =

0.50

/8 = Σ B ni ? yi E * n =

<4.00

>umlah bari! tulangan,

nb ;ari! ke 1 2 #

-

#

OK!

>umlah

>arak

>uml. >arak

ni

yi

ni ? yi


#-.00 0.00 0.00 #- -0


/ = h  /8 = 55.00 a = %! ?  y *  0.35 ?  78 ? b  = 41.12# Mn = %! ?  y ?  /  a * 2  ? 10  = #25.0 φ ? Mn = 20.523 Mu@ ≥

A

mm

#.1-0

mm mm km km

AMAN OK!

%. TULANGAN MOMEN NEGATIF

Mn = Mu * φ = Momen negati nominal ren7ana, 1-./8 = iperkirakan jarak pu!at tulangan lentur ke !i!i beton, 50 / = h  /8 = 00.00 Tinggi eekti balok, 'n = Mn ? 10 *  b ? / 2  = 0.31-< aktor tahanan momen, 

'n

+

'max

km mm mm

OK!


ρ = 0.35 ?  7L *  y ? B 1  √ ? B1 C 2 ? 'n *  0.35 ?  7L  E = 0.00203 ρmin = √  78 *  4 ?  y  = 'a!io tulangan minimum, 0.00##ρ min = 1.4 *  y = 'a!io tulangan minimum, 0.00#50 ρ = 0.00#50 'a!io tulangan yang /igunakan, %! = ρ ? b ? / = )ua! tulangan yang /iperlukan, 120 2 n = %! *  π * 4 ?   = >umlah tulangan yang /iperlukan, #.#15 4  22 igunakan tulangan, %! = n ? π * 4 ? 2 = )ua! tulangan terpakai, 1521 nb = n * n! = >umlah bari! tulangan, 0.50

mm2

mm2

nb

;ari! ke 1 2 #

-

#

OK!

>umlah

>arak

>uml. >arak

ni

yi

ni ? yi


#-.00 0.00 0.00 #-

/8 = Σ B ni ? yi E * n = 50

<4.00


/ = h  /8 = 55.0 a = %! ?  y *  0.35 ?  78 ? b  = 41.12# Mn = %! ?  y ?  /  a * 2  ? 10  = #25.0 φ ? Mn = 20.523 Mu ≥

A

mm

141.##4

mm mm km km

AMAN OK!

#. TULANGAN GESER

Iaya ge!er ultimit ren7ana, aktor re/uk!i kekuatan ge!er, Tegangan leleh tulangan ge!er, Kuat ge!er beton, Tahanan ge!er beton,

Ju = φ=  y = J7 = G  78 *  ? b ? / ? 10 # = φ ∗ J7 =

1-0.554 0.0 240 #12.#40 13-.404

k MPa k k

Han0a ,er(u tu(.*eser 1in

φ ∗ J! = Ju  φ ∗ J7 = Tahanan ge!er !engkang,  J! = 1-0.554 Kuat ge!er !engkang, 2 P 1# igunakan !engkang berpenampang " % = n! ? π * 4 ? P2 = 25.4 )ua! tulangan ge!er !engkang, ! = % ?  y ? / *  J! ? 10#  = 21. >arak !engkang yang /iperlukan " !max = / * 2 = >arak !engkang mak!imum, 2-3.00 !max = >arak !engkang mak!imum, 250.00 ! = 21. >arak !engkang yang haru! /igunakan,

k k mm2 mm mm mm mm

iambil jarak !engkang " igunakan !engkang,

2

P

1#

! = 210 210

mm

Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi

ANALISIS KEKUATAN KOLOM BETON BERTULANG DENGAN DIAGRAM INTERAKSI [C]2010 : M. Noer Ilham

K6 K6)6M

K6)6M )%T%F ;%$MT

INPUT DATA KOLOM

 78 =  y = b= h= /! = n= =

25 MPa 400 MPa 400 mm 00 mm 40 mm 1# buah 1 mm

! = untuk 78 ≤ #0 MPa untuk 78 A #0 MPa N1 = 2 %! = n ? π * 4 ?  = x = h  2?/! = ρ = %! * %g =

2.@05 MPa

Kuat tekan beton, Tegangan leleh baja, )ebar kolom, Tinggi kolom, Tebal brutto !elimut beton, >umlah tulangan, iameter tulangan, PERHITUNGAN DIAGRAM INTERAKSI

Mo/ulu! ela!ti! baja, = 0.35 1 = 0.35  0.003  78  #0 1 aktor /i!tribu!i tegangan, )ua! tulangan total, >arak antara tulangan, 'a!io tulangan, aktor re/uk!i kekuatan, φ = 0.5 untuk Pn O 0.1 ? 78 ? b ? h φ = 0.30 untuk Pn = 0

&ntuk " 0

≤

0.35 214 mm2 520.00 mm 1.0<

Pn ≤ 0.1 ?  78 ? b ? h

φ = 0.5 @ 0.15 ?  P no  Pn  * Pno


N2 Luas 1asin*&1asin* tu(an*an

%!1 = 2*4 ? %! = 1#0- mm2 %!2 = 2*4 ? %! = 1#0- mm2 %! = 214 mm2 Pa/a kon/i!i tekan ak!ial !entri! Mno = 0 " 1 2

Jara tu(an*an t3). sisi bet2n

/1 = x @ /! = /2 = /! =

50 mm 40 mm

Pno = 0.30?B 0.35? 78 ?b?h @ %!? y  0.35? 78E?10# = 43-2 k 0.1 ?  78 ? b ? h ?10 # = 00 k 7 = 7b = 00 * 00 @  y ? /1 = ##.0 mm Pa/a kon/i!i balan7e " Pa/a kon/i!i gari! netral terletak pa/a jarak 7 /ari !i!i beton tekan terluar " 'egangan pa/a ma!ingma!ing baja tulangan " !i = 0.00# ?  7  / i  * 7 Tegangan pa/a ma!ingma!ing baja tulangan " Q !i Q maka " !i = ε!i? ! &ntuk Q !i Q maka " !i =Q !i Q * ε!i?  y &ntuk → >umlah interal jarak gr! netral = 112 ∆7 = 5.#5-1 URAIAN PERHITUNGAN

PERSAMAAN

UNIT

Iayagaya internal pa/a ma!ingma!ing baja tulangan " 'e!ultan gaya internal baja tulangan " Momen akibat gaya internal ma!ingma!ing baja tulangan " Momen total akibat gaya internal baja tulangan " Tinggi blok tegangan tekan beton, Iaya internal pa/a beton tekan " Momen akibat gaya internal tekan beton " Iaya ak!ial nominal " Momen nominal " Iaya ak!ial ren7ana "

!i = %!i ?  !i ? 10 9! = B Σ !i E?10# M!i = !i?h*2  /i M! = Σ M!i a = N1 ? 7 97 = 0.35 ?  78 ? b ? a ? 10 # M7 = 97 ? h  a * 2 Pn = 9! @ 97 Mn = M7 @ M!?10# Pu = φ ? Pn #

k k kmm kmm mm k kmm k km k


Mu = φ ? Mn

Momen ren7ana "

km

1000 <50 <00 350 300 -50 -00

b = 400 mm h = 00 mm

50 00

"#

550

D

"4

 78 = 25 MPa  y = 400 MPa

500

φ.Πν (κΝ)

450 400

Pu

Mu

#50

k

km

#00

112.

11.-

250

12<.-

10.-

200

124.0

11.<

150

32.3

1#.0

100

1#.0

1#.5

50

11.5

10.2

114.2

15.-

-2.<

1-.#

0 0

2

4



3

10 1 2 1 4 1 13 20 22 24 2 2 3 #0 # 2 # 4 # #3 40 42 44 4 4 3 5 0


φ.Μν (κΝµ)

ANALISIS KOLOM DENGAN DIAGRAM INTERAKSI 7



!1



!2

mm







MPa

MPa

k

!1

!2

!1



!2

k

9

!

k

M

M

M

a

9

kmm

kmm

kmm

mm

k

!1

!2

!

7

M

7

kmm

KONDISI TEKAN AKSIAL SENTRIS

SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS

0.00045 0.0004# 0.00041 0.000#< 0.000#0.000#5 0.000#2 0.000#0 0.00023 0.00025 0.0002# 0.00020 0.00013 0.00015 0.0001# 0.00010 0.00000.00005 0.00002 0.00001 0.00004 0.00000.00010 0.0001# 0.0001 0.0001< 0.0002# 0.0002 0.0002< 0.000## 0.000# 0.00040 0.00044

0.00232 0.00232 0.00232 0.00231 0.00231 0.00231 0.00231 0.00231 0.00231 0.00230 0.00230 0.00230 0.00230 0.00230 0.002-< 0.002-< 0.002-< 0.002-< 0.002-< 0.002-< 0.002-3 0.002-3 0.002-3 0.002-3 0.002-0.002-0.002-0.002-0.002- 0.002- 0.002- 0.002- 0.002-5

<0.<1 3.-4 32.51 -3.20 -#.3# <.#4.35 0.24 55.5 50.-< 45.<4 41.00 #5.<#0.35 25.4 20.## 14.<# <.42 #.30 1.<2 -.-5 1#.-0 1<.- 25.<5 #2.2 #3.-0 45.251.<3 53.32 5.32 -2.< 30.2 3-.-2

400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00

113.31 11#.# 10-.3# 102.20 <.43 <0. 34.-5 -3.-# -2.1 .#3 0.0# 5#.53 4-.01 40.#2 ##.51 2.51<.51 12.#1 4.<2.51 10.1# 1-.<0 25.3# ##.<1 42.1 50.55<.1 -.<# -.33 3.02 <5.#5 104.3< 114.4

522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.-

41.5#.1# #0.5< 24.< 1<.24 1#.4# 0-.51 01.4< 5<5.#53<.14 532.30 5-.#4 5<.-5#.03 55.254<.## 542.25#5.052-.-# 520.25 512.# 504.3 4<.<# 433.35 430.0 4-2.1< 4#.0 454.3# 445.33 4#.-4 42-.41 41-.3403.12

#03<0.42 1#5<1-.3 2<4-4.32 1#5<1-.3 230#5.3 1#5<1-.3 25-2.< 1#5<1-.3 25035.51 1#5<1-.3 2#5-2.<0 1#5<1-.3 220#4.4- 1#5<1-.3 204<.5 1#5<1-.3 133--.43 1#5<1-.3 1-25-.52 1#5<1-.3 1503.<4 1#5<1-.3 1#<#0.<3 1#5<1-.3 12222.3# 1#5<1-.3 1043#.3 1#5<1-.3 3-12.3 1#5<1-.3 <03.<5 1#5<1-.3 50-1.5 1#5<1-.3 #1<<.5- 1#5<1-.3 12<1.<< 1#5<1-.3 52.20 1#5<1-.3 2#4.0- 1#5<1-.3 454.-2 1#5<1-.3 -15.#1 1#5<1-.3 331-.0# 1#5<1-.3 10<1.12 1#5<1-.3 1#143.33 1#5<1-.3 15#31.5 1#5<1-.3 1-0.35 1#5<1-.3 1<<3-.<2 1#5<1-.3 22#4.40 1#5<1-.3 24-<1.3< 1#5<1-.3 2-2-2.02 1#5<1-.3 2<30.55 1#5<1-.3

10502-.44 1044#.04 10-332.00 10<#44.<0 1103#2.#5 112#44.<11#33#.40 115443.#1 11-040.#3 1130.#4 120#03.<2 121<3.3< 12#<5.04 1254#4.13 12-205.13 12<003.<2 1#034.#0 1#2-13.2< 1#425.31#5-0.0 1#3551.<# 1405-2.5< 142##.1144-#4.3< 143-3.<3 14<0.-4 1512<<.52 15#5-3.-1 155<05.-< 153232.210-0<.-5 1#13<.3< 15-24.41

51.00 55.45 551.3< 54-.#4 542.-< 5#3.2# 5##.3 52<.1# 524.5520.02 515.4 510.<1 50.# 501.30 4<-.25 4<2.-0 433.14 43#.5< 4-<.04 4-4.43 4<.<# 45.#3 40.32 45.2451.-1 44-.1 442.1 4#3.05 4##.50 423.<5 424.#< 41<.34 415.2<

4-3.50 <2<35.-5 4-2<.-< 102<<<.-2 4<1.0< 1123#-.45 452.#3 1224<3.<# 41#.3 1#1<34.1 45-4.<- 1412<#.15 45#.2- 150425.33 44<-.5 15<#32.#4453.3 1312.1 4420.15 1--.1 4#31.45 1351<4.#5 4#42.-4 1<#445.35 4#04.04 201521.10 425.## 20<420.10 422.# 21-142.3 413-.<2 2243<.#414<.21 2#205<.# 4110.51 2#<25#.4 40-1.30 242-1.41 40##.10 25#112.<2 #<<4.#< 25<--3.1< #<55.< 22-.21 #<1.<3 2-25-<.<< #3-3.23 2-3-1.52 #3#<.5- 234-.30 #300.3- 2<040.3# #-2.1 2<03.1 #-2#.4 #01500.15 #34.-5 #0-55.44 #4.04 #113#4.43 #0-.#4 #1-#-.2#53.# #214#.32 #52<.<# #2014.12

Pn k 43-1.<3 43-1.<3 43-1.<3 43-1.<3 43-1.<3 43-1.<3 43-1.<3 43-1.<3 43-1.<3 43-1.<3 43-1.<3 43-1.<3 43-1.<3 43-1.<3 4323.41 4-32.<0 4-#-.25 4<1.43 445.53 45<<.5# 455#.#5 450-.02 440.55 441#.<2 4#-.1# 4#20.142-#.05 4225.- 41-3.2< 41#0.# 4032.-< 40#4.-5 #<3.50 #<#3.05

Mn km 0.00 1<3.01 20<.44 220.-2 2#1.34 242.32 25#.4 24.#1 2-4.3# 235.20 2<5.4# #05.50 #15.4# #25.22 ##4.35 #44.#5 #5#.-0 #2.<1 #-1.<#30.<0 #3<.3 #<3.## 40.34 415.21 42#.45 4#1.5 4#<.5# 44-.#455.03 42. 4-0.12 4--.45 434.5 4<1.-4

R 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

R.Pn k #1.-< #1.-< #1.-< #1.-< #1.-< #1.-< #1.-< #1.-< #1.-< #1.-< #1.-< #1.-< #1.-< #1.-< #1#3.4#103.33 #0-<.21 #04<.4 #01<.2 2<3<.-0 2<5<.3 2<2<.5 23<<.#5 23<.04 23#3.# 2303.11 2---.4< 2-4.-4 2-15.3< 234.<1 25#.31 222.5< 25<1.2# 255<.-#

R.Mn km 0.00 123.-1 1#.14 14#.4150.-0 15-.3# 14.3 1-1.30 1-3.4 135.#3 1<2.0# 1<3.53 205.0# 211.#< 21-. 22#.3# 22<.<0 2#5.3< 241.-3 24-.53 25#.2< 253.<1 24.45 2<.3< 2-5.24 230.51 235.< 2<0.-< 2<5.30 #00.-# #05.53 #10.#4 #15.02 #1<.#


7 mm SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS



!1

0.00043 0.00052 0.0005 0.0000 0.0004 0.0003 0.000-2 0.000-0.00032 0.0003 0.000<1 0.000< 0.00101 0.0010 0.00112 0.00110.0012# 0.00123 0.001#4 0.00140 0.00140.0015# 0.0010 0.0010.001-4 0.00131 0.00133 0.001< 0.00204 0.00212 0.00221 0.002#0 0.002#< 0.00243 0.00253 0.0023 0.002-<



!2

0.002-5 0.002-5 0.002-5 0.002-4 0.002-4 0.002-4 0.002-# 0.002-# 0.002-# 0.002-2 0.002-2 0.002-2 0.002-1 0.002-1 0.002-1 0.002-0 0.002-0 0.002< 0.002< 0.002< 0.0023 0.0023 0.0020.0020.002 0.002 0.0025 0.0025 0.0024 0.002# 0.002# 0.0022 0.0022 0.0021 0.0020 0.0025< 0.0025<



!1

MPa <5.#4 10#.14 111.11 11<.212-.1 1#.15 144.3< 15#.35 1#.02 1-2.41 132.04 1<1.<2 202.05 212.44 22#.10 2#4.04 245.23 25.3# 23.-0 230.<0 2<#.45 #0.# #1<.5 ###.## #4-.4# #1.< #-.<5 #<2.41 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00



!2

MPa 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00



!1

k 124.0 1#4.-< 145.21 155.31.-1--.<4 13<.# 201.0 21#.05 225.## 2#-.<1 250.32 24.05 2--.# 2<1.5#05.3#20.5 ##5.5 #51.1 #-.11 #3#.51 400.#3 41-.-5 4#5.# 454.0 4-#.05 4<2.# 512.34 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.-



!2

k 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.-

9

!

M

!1

M

!2

k kmm kmm #<3.1 #2#<-.2- 1#5<1-.3 #3-.<- #504.0< 1#5<1-.3 #--.55 #--54.< 1#5<1-.3 #.3< 40525.<- 1#5<1-.3 #55.<< 4##1.2- 1#5<1-.3 #44.3# 42#.12 1#5<1-.3 ###.40 4<2##.<1 1#5<1-.3 #21.-0 522-.10 1#5<1-.3 #0<.-1 55#<2.#2 1#5<1-.3 2<-.4# 53535.2< 1#5<1-.3 234.35 135-.33 1#5<1-.3 2-1.<4 521#.12 1#5<1-.3 253.-1 354.1 1#5<1-.3 245.1# -2134.# 1#5<1-.3 2#1.1< -530-.21 1#5<1-.3 21.3< -<52.41 1#5<1-.3 202.20 3##45.3 1#5<1-.3 13-.11 3-2<.- 1#5<1-.3 1-1.0 <1#02.1- 1#5<1-.3 155.5 <544-.<4 1#5<1-.3 1#<.25 <<-11.32 1#5<1-.3 122.#3 1040<3.<4 1#5<1-.3 105.01 10314.-2 1#5<1-.3 3-.1# 11#24.3< 1#5<1-.3 3.-0 113055.55 1#5<1-.3 4<.-1 122<<#.1 1#5<1-.3 #0.1# 123034.5< 1#5<1-.3 <.<# 1####-.15 1#5<1-.3 0.00 1#5<1-.3 1#5<1-.3 0.00 1#5<1-.3 1#5<1-.3 0.00 1#5<1-.3 1#5<1-.3 0.00 1#5<1-.3 1#5<1-.3 0.00 1#5<1-.3 1#5<1-.3 0.00 1#5<1-.3 1#5<1-.3 0.00 1#5<1-.3 1#5<1-.3 0.00 1#5<1-.3 1#5<1-.3 0.00 1#5<1-.3 1#5<1-.3

M

!

kmm 13#15.14 1-0<#.<5 1-#-2.3# 1-44#.3# 1-<2-<.1# 132130.<< 135151.-1331<#.<1<1#10.13 1<450#.15 1<---5.-5 2011#0.<3 2045-2.0# 203102.22 211-25.0215444.221<2#.-2 22#13-.5# 22-220.0# 2#1#5.30 2#52<.< 24001.31 2445#2.53 24<132.-5 25#<-#.41 253<11.02 24002.4 2<255.01 2-13#5.-# 2-13#5.-# 2-13#5.-# 2-13#5.-# 2-13#5.-# 2-13#5.-# 2-13#5.-# 2-13#5.-# 2-13#5.-#

a mm 410.-# 40.13 401.# #<-.0#<2.52 #3-.< #3#.41 #-3.3 #-4.#0 #<.-5 #5.20 #0.4 #5.0< #51.54 #4.<3 #42.4# ##-.33 ###.#2 #23.-#24.21 #1<. #15.11 #10.55 #0.00 #01.45 2<.3< 2<2.#4 23-.-< 23#.2# 2-3.3 2-4.1# 2<.525.02 20.4 255.<1 251.# 24.30

9

7

M

7

k kmm #4<1.22 ##0#33.1#452.52 ##4535.<#41#.31 ##30-.5# ##-5.11 #42452.34 ###.40 #4121.<0 #2<-.-0 #4<14.-1 #253.<< #52<#1.2#220.2< #50-1.5< #131.53 #5<0#5. #142.33 #132#.43 #104.1- #44#5.0 #05.4 #3-0.#< #02.- #<12<.42<33.05 #-1212.#0 2<4<.#5 #-#113.33 2<10.4 #-434<.22 23-1.<4 #-40#.#1 23##.2# #---31.15 2-<4.5# #-3<32.-4 2-55.32 #30003.0< 2-1-.12 #3035-.1< 2-3.41 #315#0.04 2#<.-1 #3202.4 201.00 #32#4-.00 252.2< #324<1.11 252#.5< #32453.<2434.33 #32250.53 244.13 #3135.<5 240-.4- #31#05.02#3.-- #305-.<4 2##0.0 #-<54.5 22<1.# #-354.<# 2252.5 #--2<<.0 221#.<5 #-535.<4 21-5.24 #-42#3.521#.54 #-244#.< 20<-.3# #-04-#.0<

Pn k #33<.#3 #340.4< #-<1.# #-42.00 #<2.#< #42.52 #5<2.#< #541.<3 #4<1.2< #440.#1 ##3<.02 ###-.41 #235.4#2##.13 #130.54 #12-.5# #0-4.14 #020.#4 2<.1# 2<11.4235.#2300.-< 2-44.-2 233.1# 2#1.00 25-#.#0 2515.01 245.10 240-.42#3.-2##0.0 22<1.# 2252.5 221#.<5 21-5.24 21#.54 20<-.3#

Mn km 4<3.-0 505.55 512.23 513.<0 525.40 5#1.30 5#3.03 544.2550.#5 55.## 52.21 53.00 5-#.-0 5-<.#1 534.34 5<0.2< 5<5.00.<0.20 11.#1.4< 21.55 2.5 #1.5# #.4 41.#4.25 51.12 5#.14 52.40 51.4< 50.40 4<.1# 4-.< 4.044.23 42.#1

R

R.Pn

R.Mn

0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

k 2523.10 24<.#2 244.#< 24#2.#0 2400.05 2#-.4 2##5.05 2#02.2< 22<.#4 22#.20 2202.3 21<.#1 21#5.55 2101.520-.#5 20#2.<0 1<<3.1< 1<#.22 1<2-.<3 13<2.4 135.4 1320.51 1-34.01-4-.23 1-10.15 1-2.4 1#4.- 15<.4154.3 15#<.-0 1514.54 143<.#3 144.22 14#<.0141#.<1 1#33.-5 1##.5<

km #24.1 #23.1 ##2.<3 ##-.23 #41.51 #45.#4<.-5 #5#.-#5-.-2 #1.1 #5.44 #<.20 #-2.<1 #-.55 #30.15 #3#.< #3-.13 #<0.# #<4.0# #<-.#< 400.-2 404.01 40-.2 410.4< 41#.-0 41.3< 420.0 42#.2# 424.54 424.0 42#.4422.- 421.<4 421.00 41<.<5 413.-3 41-.50


7 mm SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS



!1

0.0023< 0.00#01 0.00#1# 0.00#25 0.00##0.00#51 0.00#4 0.00#-< 0.00#<4 0.00410 0.0042 0.0044# 0.0041 0.00430 0.00500 0.00521 0.0054# 0.005 0.005<1 0.0010.0045 0.00-4 0.00-05 0.00-#3 0.00--4 0.00312 0.0035# 0.003<0.00<44 0.00<< 0.01052 0.010# 0.010-4 0.0#2#-



!2

0.00253 0.00250.0025 0.00255 0.00254 0.00254 0.0025# 0.00252 0.00250 0.0024< 0.00243 0.00240.0024 0.00244 0.0024# 0.00241 0.00240 0.002#3 0.002# 0.002#5 0.002## 0.002#0 0.00223 0.0022 0.0022# 0.00221 0.00213 0.00215 0.00211 0.00200.0020# 0.0020# 0.00202 0.0004-



!1

MPa 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00



!2

MPa 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 400.00 <4.-4



!1

k 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.- 522.-

KONDISI TEKAN AKSIAL KECIL 5 Pn 6 7." 8 9:/ 8 b 8 3



!2

9

!

M

!1

k k kmm 522.- 0.00 1#5<1-.3 522.- 0.00 1#5<1-.3 522.- 0.00 1#5<1-.3 522.- 0.00 1#5<1-.3 522.- 0.00 1#5<1-.3 522.- 0.00 1#5<1-.3 522.- 0.00 1#5<1-.3 522.- 0.00 1#5<1-.3 522.- 0.00 1#5<1-.3 522.- 0.00 1#5<1-.3 522.- 0.00 1#5<1-.3 522.- 0.00 1#5<1-.3 522.- 0.00 1#5<1-.3 522.- 0.00 1#5<1-.3 522.- 0.00 1#5<1-.3 522.- 0.00 1#5<1-.3 522.- 0.00 1#5<1-.3 522.- 0.00 1#5<1-.3 522.- 0.00 1#5<1-.3 522.- 0.00 1#5<1-.3 522.- 0.00 1#5<1-.3 522.- 0.00 1#5<1-.3 522.- 0.00 1#5<1-.3 522.- 0.00 1#5<1-.3 522.- 0.00 1#5<1-.3 522.- 0.00 1#5<1-.3 522.- 0.00 1#5<1-.3 522.- 0.00 1#5<1-.3 522.- 0.00 1#5<1-.3 522.- 0.00 1#5<1-.3 522.- 0.00 1#5<1-.3 522.- 0.00 1#5<1-.3 522.- 0.00 1#5<1-.3 12#.31 #<3.<5 1#5<1-.3

M

!2

kmm 1#5<1-.3 1#5<1-.3 1#5<1-.3 1#5<1-.3 1#5<1-.3 1#5<1-.3 1#5<1-.3 1#5<1-.3 1#5<1-.3 1#5<1-.3 1#5<1-.3 1#5<1-.3 1#5<1-.3 1#5<1-.3 1#5<1-.3 1#5<1-.3 1#5<1-.3 1#5<1-.3 1#5<1-.3 1#5<1-.3 1#5<1-.3 1#5<1-.3 1#5<1-.3 1#5<1-.3 1#5<1-.3 1#5<1-.3 1#5<1-.3 1#5<1-.3 1#5<1-.3 1#5<1-.3 1#5<1-.3 1#5<1-.3 1#5<1-.3 #21<1.0-

M

!

kmm 2-13#5.-# 2-13#5.-# 2-13#5.-# 2-13#5.-# 2-13#5.-# 2-13#5.-# 2-13#5.-# 2-13#5.-# 2-13#5.-# 2-13#5.-# 2-13#5.-# 2-13#5.-# 2-13#5.-# 2-13#5.-# 2-13#5.-# 2-13#5.-# 2-13#5.-# 2-13#5.-# 2-13#5.-# 2-13#5.-# 2-13#5.-# 2-13#5.-# 2-13#5.-# 2-13#5.-# 2-13#5.-# 2-13#5.-# 2-13#5.-# 2-13#5.-# 2-13#5.-# 2-13#5.-# 2-13#5.-# 2-13#5.-# 2-13#5.-# 13103.<4

a mm 242.25 2#-.-0 2##.14 223.5< 224.04 21<.43 214.<# 210.#3 205.32 201.21<.-1 1<2.1 13-.1 13#.05 1-3.50 1-#.<5 1<.#< 14.34 10.2< 155.-# 151.13 14.# 142.01#-.52 1#2.< 123.41 12#.3 11<.#0 114.-5 110.20 105.4 104.-< 10#.<4 40.#3

9

7

M

7

k kmm 205<.1# #3#25.<3 2020.42 #002.# 1<31.-1 ##50#.02 1<4#.01 #032-.11<04.#0 #5-<-5.0135.0 #54<4.-2 132.3< #51-42.12 1-33.1< #43#1.23 1-4<.43 #44304.1< 1-10.-3 #410-0.35 1-2.0- ##-11.2 1##.#- ###0-5.4# 15<4. #2331#.#4 1555.< #24#-5.01 151-.25 #1<-0.44 14-3.54 #14<<.1 14#<.34 #10002.54 1401.1# #0435<.22 1#2.4# 2<<5#<.5 1#2#.-2 2<404#.34 1235.02 233#-1.-3 124.#1 23252#.4 120-.1 2-4<3.<1 113.<0 2-02<3.10 11#0.20 2#<21.05 10<1.4< 25-#-.-5 1052.-< 250#3.20 1014.03 24#-#2.40 <-5.#3 2#50.# <#.- 22<#<2.03<-.< 221<5-.5# 3<0.-4 220550.2# 33#.51 21<1#.-< #4#.1< <023.15

Pn k 205<.1# 2020.42 1<31.-1 1<4#.01 1<04.#0 135.0 132.3< 1-33.1< 1-4<.43 1-10.-3 1-2.01##.#15<4. 1555.< 151-.25 14-3.54 14#<.34 1401.1# 1#2.4# 1#2#.-2 1235.02 124.#1 120-.1 113.<0 11#0.20 10<1.4< 1052.-< 1014.03 <-5.#3 <#.3<-.< 3<0.-4 33#.51 55.-

Mn km 40.1 #-.34 #5.#4 #2. 2<.31 2.-3 2#.53 20.20 1.4 12.<1 0<.00 04.<1 00.5 5<.21 5<1.0 53.31 531.34 5-.< 5-1.#3 55.33 50.21 554.# 543.## 542.1# 5#5.- 52<.20 522.4515.5503.4< 501.2# 4<#.-< 4<2.#< 4<0.<24.14

R

R.Pn

R.Mn

0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.31

k 1##3.4# 1#1#.21233.11 122.< 12#-.30 1212.4 113-.43 112.#2 11#-.1 1112.00 103.35 101.< 10#.5# 1011.#<3.21 <1.05 <#5.<0 <10.-4 335.53 30.42 3#5.2 310.10 -34.<4 -5<.-< -#4.# -0<.434.#1 5<.15 ##.<< 03.34 53#.3 5-3.<3 5-4.23 45.#<

km 41.11 414.5< 412.<411.2# 40<.#3 40-.41 405.## 40#.1# 400.32 #<3.#< #<5.35 #<#.1< #<0.42 #3-.54 #34.54 #31.42 #-3.1< #-4.35 #-1.#< #-.32 #4.1# #0.## #5.42 #52.#< #43.24 #4#.<3 ##<.1 ##5.12 ##0.52 #25.30 #20.<#20.05 #1<.1# 214.<<

#<0.00 #<0.00

0.00 50.00


7



!1



mm

!2









MPa

MPa

k

k

!1

!2

!1

!2

9

!

k

M

!1

kmm

M

!2

kmm

M

a

9

kmm

mm

k

2-13#5.-#

235.0

!

7

M

Pn

Mn

kmm

k

km

242-.0

5#.45

7

R

R.Pn

R.Mn

k

km

KONDISI BALANCE

SSS 0.00200 0.0024 400.00 400.00 522.-

522.-

0.00 1#5<1-.3 1#5<1-.3

242-.0 #3113.-2

0.5

0.00 15--.<4

0.00 424.-5

Maka s diambil 300 mm. Tipe

Lx (mm)

Ly (mm)

Ly/Lx

1(III)

2150

2650

123,255,814

2(IX)

1150

2150

1,869,565,217

3 (III)

2150

3000

1,395,348,837

4(VIII)

1000

2450

2,45

5(II)

1650

2450

1,484,848,485

6(II)

1150

2450

2,130,434,783

7(IX)

950

2000

2,105,263,158

8(IX)

1500

2000

1,333,333,333

9

1000

3550

3,55

10

1050

2800

2,666,666,667

11(IX)

2500

2800

1,12

12(VIII)

1050

2000

1,904,761,905

13(VI)

2200

3550

1,613,636,364

14(VIII)

1000

1350

1,35

15(IX)

1350

2800

2,074,074,074

16(III)

2250

3800

1,688,888,889

17(V)

2000

2250

1,125

18(III)

2200

3600

1,636,363,636

Tipe

Mlx/Φ (N mm)

Mly/Φ (N mm)

/Φ (N m

Mty/Φ (N mm)

Mtix/Φ

1(III)

1568298,69

1032782,06

213099,7

2830587,88

2(IX)

612846,50

186042,69

902854,22

580015,44

3 (III)

1989061,75

879777,31

710365,1

2945341,44

9945

4(VIII)

653725,00

132400,00

001275,0

604075,00

3268

5(II)

1025055,28

371723,34

689651,5

1225560,60

6(II)

634733,88

164155,31

897382,38

580015,44

7(IX)

433154,88

126959,19

619859,56

395813,94

8(IX)

763368,75

372375,00

359168,7

1024031,25

9

591250

-

918750

-

517

10

651250

-

1012500

-

570

11(IX)

1680859,38

1189531,25

361718,7

2818671,88

12(VIII)

611253,56

159655,78

012673,8

693362,25

3056

13(VI)

2843621,00

1201530,00

-

4445661,00

14218

14(VIII)

388925,00

190325,00

728200,00

612350,00

1944

15(IX)

874708,88

256380,19

251738,5

769140,56

16(III)

2681100,00

879735,94

587194,5

3225698,44

17(V)

1324000,00

662000,00

515600,0

-

18(III)

2563264,00

841071,00

385584,5

3083927,00

7841

13405 12816

Tipe

Aslx

Asly

Astx

Asty

ρlx

ρly

ρtx

ρty

1(III)

54,09

41,05

111,86

114,08

0,00054

0,00041

0,00112

0,00114

2(IX)

21,02

7,35

31,02

22,98

0,00021

0,00007

0,00031

0,00023

3 (III)

68,76

34,93

129,55

118,81

0,00069

0,00035

0,00130

0,00119

4(VIII)

22,43

5,23

34,42

23,94

0,00022

0,00005

0,00034

0,00024

5(II)

35,24

14,70

58,31

48,79

0,00035

0,00015

0,00058

0,00049

6(II)

21,78

6,48

30,83

22,98

0,00022

0,00006

0,00031

0,00023

7(IX)

14,84

5,01

21,26

15,66

0,00015

0,00005

0,00021

0,00016

8(IX)

26,21

14,73

46,82

40,70

0,00026

0,00015

0,00047

0,00041

9

20

-

32

-

0,0002

-

0,00032

-

10

22

-

35

-

0,00022

-

0,00035

-

11(IX)

58,01

47,34

117,14

113,59

0,00058

0,00047

0,00117

0,00114

12(VIII)

20,97

6,31

34,82

27,49

0,00021

0,00006

0,00035

0,00027

13(VI)

98,79

47,82

-

181,49

0,00099

0,00048

-

0,00181

14(VIII)

13,33

7,52

25,00

24,27

0,00013

0,00008

0,00025

0,00024

15(IX)

30,05

10,13

43,09

30,51

0,00030

0,00010

0,00043

0,00031

16(III)

93,06

34,93

161,00

130,41

0,00093

0,00035

0,00161

0,00130

17(V)

45,60

26,24

87,23

-

0,00046

0,00026

0,00087

-

18(III)

88,91

33,39

153,74

124,53

0,00089

0,00033

0,00154

0,00125

minimum , sehingga diambil ρ minimum sebesar 0,00! sebagai tulangan susut dan suhu. "engan ρ # 0,00! didapatk an spasi antar tulangan sebesar $00 mm, tetapi jarak ma%imu m antar tulangan adalah 3t atau $00 mm, diambil spasi sebesar 3t &300 mm'

Pada kolom tipe slab tabel di atas, terdapat keterangan jenis slab, berikut penjelasan dari je Slab Jenis : Slab dengan keempat sisi menerus. : Slab dengan satu sisi panjang menerus, satu sisi panja Slab Jenis: Slab dengan dua sisi panjang menerus dan dua sisi pendek tidak menerus. Slab Jenis: Slab dengan satu sisi pendek menerus dan ketiga sisi lainnya tidak menerus. Slab Jenis: Slab dengan satu sisi panjang tidak menerus dan ketiga sisi lainnya menerus. Slab Jenis: Slab dengan satu sisi pendek tidak menerus dan ketiga sisi lainnya menerus.

Jenis Dua arah Dua arah Dua arah Dua arah Dua arah Dua arah Dua arah Dua arah Satu arah Satu arah Dua arah Dua arah Dua arah Dua arah Dua arah Dua arah Dua arah Dua arah (N mm) 9,34

y/Φ (N mm) 516391,03 93021,34

0,88

439888,66

2,50

63479,59 186187,50

500

-

000

594765,63

6,78

-

10,50

600765,00

2,50

128190,09

50,00

439867,97 331000,00

32,00

420535,50

is slab.

g tidak menerus, satu sisi pendek menerus, dan satu sisi pendek tidak menerus


ANALISIS KEKUATAN KOLOM BETON BERTULANG DENGAN DIAGRAM INTERAKSI KOLOM GIS ";7 K< KEMBANGAN II

K6 K6)6M

kolom ba!ement

INPUT DATA KOLOM

 78 =  y = b= h= /! = n= =

Kuat tekan beton, Tegangan leleh baja, )ebar kolom, Tinggi kolom, Tebal brutto !elimut beton, >umlah tulangan, iameter tulangan,

25 MPa 400 MPa 400 mm 00 mm 40 mm 14 buah 1 mm

PERHITUNGAN DIAGRAM INTERAKSI

! = 2.@05 MPa untuk 78 ≤ #0 MPa untuk 7 8 A #0 MPa N1 = 0.35 aktor /i!tribu!i tegangan, %! = n ? π * 4 ? 2 = 2315 mm2 )ua! tulangan total, x =  h  2?/!  * 2 = 1#0.000 mm >arak antara tulangan, 'a!io tulangan, ρ = %! * %g = 1.1- aktor re/uk!i kekuatan, &ntuk " 0 ≤ Pn ≤ 0.1 ?  78 ? b ? h φ = 0.5 untuk Pn O 0.1 ? 78 ? b ? h φ = 0.5 @ 0.15 ?  P no  Pn  * Pno φ = 0.30 untuk Pn = 0 Mo/ulu! ela!ti! baja, N1 = 0.35 N1 = 0.35  0.003  78  #0



1000 <50 <00 350 300 -50 -00 50 00

b= h=

400 00

mm mm

"$

D

"4

 78 =  y =

25 400

Tul. "

550 500

φ.Πν (κΝ)

450 400

Pu

Mu

#50

k

km

#00

112.54

2#.#20

250

12<.-03

21.#14

200

124.013

2#.33

150

32.32<

25.<15

100

1#.043

2.<<#

50

11.54<

20.454

114.222

#1.#22

-2.350

#4.-3

0 0

2

4



3

10 12 14 1 13 20 22 24 2 23 #0 #2 #4 # #3 40 42 44 4 43 50

φ.Μν (κΝµ)

ANALISIS KOLOM DENGAN DIAGRAM INTERAKSI

MPa MPa


N2

Luas 1asin*&1asin* tu(an*an


/1 = 4?x @ /! = 304 mm2 50 mm P no = 4<## k /2 = #x @ /! = → 402 mm2 4#0 mm /2 = 2x @ /! = 0.1 ? 78 ? b ? h ?10 # = 00 k 402 mm2 #00 mm /2 = x @ /! = 402 mm2 1-0 mm Pa/a kon/i!i balan7e " 2 /# = /! = @  y ? /1 = ##.00 mm 304 mm 40 mm = 7b = 00 * 00 2315 mm2 Pa/a kon/i!i gari! netral terletak pa/a jarak 7 /ari !i!i beton tekan terluar " !i = 0.00# ?  7  / i  * 7 'egangan pa/a ma!ingma!ing baja tulangan " Tegangan pa/a ma!ingma!ing baja tulangan " Q !i Q +  y * ! maka "  !i = ε!i? ! &ntuk Q !i Q ≥  y * ! maka "  !i =Q !i Q * ε!i?  y &ntuk → >umlah interal jarak gr! netral = 100 ∆7 = .0000 1 2 # 4 5

%!1 = 4*14 ? %! = %!2 = 2*14 ? %! = %!2 = 2*14 ? %! = %!2 = 2*14 ? %! = %!# = 4*14 ? %! = %! =

Pa/a kon/i!i tekan ak!ial !entri! Mno = 0 " Pno = 0.30?B 0.35? 78 ?b?h @ %!? y  0.35? 78E

URAIAN PERHITUNGAN

PERSAMAAN

UNIT

Iayagaya internal pa/a ma!ingma!ing baja tulangan " 'e!ultan gaya internal baja tulangan " Momen akibat gaya internal ma!ingma!ing baja tulangan " Momen total akibat gaya internal baja tulangan " Tinggi blok tegangan tekan beton, Iaya internal pa/a beton tekan " Momen akibat gaya internal tekan beton " Iaya ak!ial nominal " Momen nominal " Iaya ak!ial ren7ana "

!i = %!i ?  !i ? 10 9! = B Σ !i E?10# M!i = !i?h*2  /i M! = Σ M!i a = N1 ? 7 97 = 0.35 ?  78 ? b ? a ? 10# M7 = 97 ? h  a * 2 Pn = 9! @ 97 Mn = M7 @ M!?10# Pu = φ ? Pn #

k k kmm kmm mm k kmm k km k



4000 #300 #00 #400 #200 #000 2300 200 2400

b= h=

400 00

mm mm

"$

D

"4

 78 =  y =

25 400

Tul. "

2200

φ.Πν (κΝ)

2000 1300 100

Pu

Mu

1400

k

km

1200 1000 300 00 400 200 0 0

20

40

0

30 100 120 140 10 130 200 220 240 20 230 #00 #20 #40 #0 #30 400

φ.Μν (κΝµ)

112.54

2#.#20

12<.-03

21.#14

124.013

2#.33

32.32<

25.<15

1#.043

2.<<#

11.54<

20.454

114.222

#1.#22

-2.350

#4.-3

MPa MPa


Momen ren7ana "   7 !1

Mu = φ !2



!#



!4



!5

mm

Mn















MPa

MPa

MPa

MPa

MPa

k

k

<0.<0< 3.2#< 31.431 -.# -1.<3 .1.5#3 5.#11 50.<30 45.545 40.000 #4.#4# 23.5-1 22.30 1.10.52 4.255 2.151 3.< 15.#35 22.222 2<.21# #.#4 4#.-3 51.1# 53.324 .-4.<< 32.<2<1.#53 100.000 103.31 11-.<4< 12-.2-# 1#.342

20<.0<1 205.505 201.352 1<3.1#1 1<4.#40 1<0.4- 13.5#3 132.524 1-3.4#1 1-4.251-0.000 15.511.224 15.-01 152.03# 14-.#3 142.55# 1#-.#4 1#2.0< 12-.4-# 122.222 11.354 111.#4 105.-4100.000 <4.113 33.0<5 31.<23 -5.10 <.1# 2.500 55.< 43.-13 41.553 #4.211

#2-.2-# #24.--1 #22.222 #1<.2 #1.<31 #14.23 #11.5#3 #03.-#3 #05.332 #02.<-0 #00.000 2<.<-0 2<#.3-3 2<0.-22 23-.500 234.211 230.351 2--.41< 2-#.<1# 2-0.##0 2.22.<21 25<.0<1 255.1-2 251.1# 24-.05< 242.352#3.554 2#4.14 22<.#0 225.000 220.25# 215.#35 210.#<0 205.2#

!1

!2

!#

!4

!5

!1

!2



!#

km  !4

k

k

1#1.04 1#0.5<3 12<.5-# 123.52< 12-.4 12.#32 125.2-124.151 12#.00# 121.3#2 120.#11<.41< 113.1-5 11.<0 115.11 114.233 112.<#111.55110.14103.-0 10-.2## 105.-2104.13102.11 100.<<< <<.#43 <-.5< <5.<23 <4.15 <2.#40 <0.4-3 33.5< 3.11 34.0# 32.541

10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 15<.3<2 153.<12 15-.<015.3-3 155.32# 154.-41 15#.#2 152.4<4 151.#2


0.000 54.000 43.000 42.000 #.000 #0.000 24.000 13.000 12.000 0.000 00.000 5<4.000 533.000 532.000 5-.000 5-0.000 54.000 553.000 552.000 54.000 540.000 5#4.000 523.000 522.000 51.000 510.000 504.000 4<3.000 4<2.000 43.000 430.000 4-4.000 43.000 42.000 45.000

0.00045 0.0004# 0.00041 0.000#3 0.000# 0.000## 0.000#1 0.00023 0.00025 0.0002# 0.00020 0.00010.00014 0.00011 0.00003 0.00005 0.00002 0.00001 0.00004 0.00003 0.00011 0.00015 0.00013 0.00022 0.0002 0.0002< 0.000## 0.000#0.00041 0.0004 0.00050 0.00054 0.0005< 0.0004 0.0003

0.00105 0.0010# 0.00101 0.000<< 0.000<0.000<5 0.000<# 0.000<1 0.0003< 0.00030.00035 0.0003# 0.00031 0.000-3 0.000- 0.000-4 0.000-1 0.000< 0.000 0.0004 0.0001 0.00053 0.0005 0.0005# 0.00050 0.00040.00044 0.00041 0.000#3 0.000#5 0.000#1 0.00023 0.00024 0.00021 0.0001-

0.0014 0.0012 0.0011 0.0010 0.00153 0.00150.0015 0.00154 0.0015# 0.00151 0.00150 0.00143 0.00140.00145 0.00144 0.00142 0.00140 0.001#< 0.001#0.001#5 0.001## 0.001#1 0.001#0 0.00123 0.0012 0.00124 0.00121 0.0011< 0.00110.00115 0.0011# 0.00110 0.00103 0.00105 0.0010#

0.0022# 0.00222 0.00221 0.00221 0.00220 0.0021< 0.00213 0.00210.00210.0021 0.00215 0.00214 0.0021# 0.00212 0.00211 0.00211 0.00210 0.0020< 0.00203 0.00200.0020 0.00204 0.0020# 0.00202 0.00201 0.00200 0.001<< 0.001<3 0.001< 0.001<5 0.001<4 0.001<2 0.001<1 0.001<0 0.00133

0.00232 0.00232 0.00231 0.00231 0.00231 0.00231 0.00231 0.00231 0.00230 0.00230 0.00230 0.00230 0.00230 0.002-< 0.002-< 0.002-< 0.002-< 0.002-3 0.002-3 0.002-3 0.002-3 0.002-3 0.002-0.002-0.002-0.002- 0.002- 0.002- 0.002- 0.002-5 0.002-5 0.002-5 0.002-4 0.002-4 0.002-4

400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 #<-. #<5.2 #<2.#<0.1 #3-.5 #34.3 #32.1 #-<.2 #-.#

400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0

-#.11# <.#55.5#1 1.#4 5-.# 5#.14<.4<2 45.233 41.001 #.2< #2.1-0 2-.21 22.<-< 13.241 1#.404 3.4 #.422 1.-#0 .<<# 12.#-# 1-.3-2 2#.4<5 2<.245 #5.123 41.143 4-.#0< 5#.10.0- .<4 -#.4-4 30.425 3-.551 <4.30 102.#5< 110.055

34.030 32.#3 31.1< -<.-# -3.14< -.5<5 -5.012 -#.#<-1.-52 -0.0-# 3.#1 .14 4.3#2 #.01# 1.15 5<.20 5-.#24 55.#4 5#.#25 51.20 4<.143 4.<<0 44.-32 42.52# 40.212 #-.34#5.425 #2.<45 #0.404 2-.301 25.1## 22.#<1<.5<1 1.-12 1#.-5-


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k

k

kmm

kmm

kmm

kmm

kmm

kmm

mm

10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350

233.-<3 232.5<# 2-.2-4 2<.3# 2#.2-25.5<# 24<.-31 242.3# 2#5.-55 223.5#4 221.13 21#.54 205.<3 1<3.10 1<0.1-1 132.014 1-#.3# 15.1-# 15.4-< 14-.5<# 1#3.50< 12<.222 11<.-2# 110.00 100.0# 3<.33-<.43.-<5-.34. #5.13 2#.415 11.#42 1.044 1#.-5-

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20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20-35.<2053.51 2052-.<# 20#<4.1# 2025.<< 2011.#1<<-2.15 1<324.13 1<-2.#2

41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33

#2-<1.###<55.4< #5141.1 ##43.<< #-5-<.1 #33##.3 40111.3 41414.35 42-4#.40 440<3.2 45430.21 43<0.03 43#23.-2 4<-<-.0# 512<5.<2 5232.#3 54#3<.#< 55<3.02 5-1-.# 5<234.55 0<33.-< 2-#1.#2 451#.4 ##.53202.03 -0111.43 -1<41.3-#31.#3 -5-#.0 ---04.2# -<-21.0 31-33.<4 3#<0<.35 3035.34 33#1<.10

!5

9

!

!1

!2

!#

!4

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

!5

!

51.00 555.<0 550.30 545.-0 540.0 5#5.50 5#0.40 525.#0 520.20 515.10 510.00 504.<0 4<<.30 4<4.-0 43<.0 434.50 4-<.40 4-4.#0 4<.20 44.10 45<.00 45#.<0 443.30 44#.-0 4#3.0 4##.50 423.40 42#.#0 413.20 41#.10 403.00 402.<0 #<-.30 #<2.-0 #3-.0

Analisis Kekuatan Ko lom Beton Bertulang Denga n Diagram Interaksi

ANALISIS KOLOM DENGAN DIAGRAM INTERAKSI 9

M

k

kmm

7

4-3.50 4-25.15 431.30 4#3.45 45<5.10 4551.-5 4503.40 445.05 4421.-0 4#-3.#5 4##5.00 42<1.5 4243.#0 4204.<5 411.0 4113.25 40-4.<0 40#1.55 #<33.20 #<44.35 #<01.50 #353.15 #314.30 #--1.45 #-23.10 #34.-5 #41.40 #5<3.05 #554.-0 #511.#5 #43.00 #424.5 ##31.#0 ###-.<5 #2<4.0

7

<2<35.-5 10413<.5 1151-2.23 125<##.<2 1#4-4.414-<#.<4 153<2.#2 1-<.2 1-425.3# 13530.< 1<50-5.00 2040-.< 2123#<.3# 221#<0.2 22<-20.#2 2#-323.<4 245-1.425##32.<2 20323.23 23052.5 2-5055.-5 2313#-.3 233#<3.33 2<4-#3.32 #0035-.#0-55.44 #124#2.12 #1-33-.-2 #2#122.2# #231#5. ##2<23.00 ##-4<<.2 #4134<.4# #45<-3.52 #4<33.52

Pn

Mn

k 4<#2.<0 4<#2.<0 4<#2.<0 4<#2.<0 4<03.2< 4353.#3 4303.#4 4-53.13 4-0-.3< 45-.45 40.33 455.14505.#0 4454.2< 440#.11 4#51.-4#00.2 4243.53 41<.-2 4144.3 40<2.44 4040.01 #<3-.##<#4.52 #331.4 #323.1 #--4.4 #-20.3#.35 #12.5#553.02 #50#.1< #443.0 ##<2.4 ###.<1 #230.34

km 0.00 125.-3 1#3.15 150.#1 12.23 1-4.05 135.# 1<-.00 203.13 21<.122<.< 240.5 250.< 21.12-1.1< 231.02 2<0. #00.11 #0<.##13.45 #2-.#4 ##.04 #44.5#52.<1 #1.03 #<.0 #-.3#34.##<1.-0 #<3.3 405.34 412.5 41<.2< 425.- 4#2.0 4#3.21

R.Pn

R 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

k #20.#< #20.#< #20.#< #20.#< #1<0.#< #15-.<5 #125.42 #0<2.32 #00.1# #02-.#5 2<<4.42<1.51 2<23.45 23<5.2< 232.02 2323.5 2-<5.12-1.53 2-2-.32<4.04 20.0< 22.01 25<1.-< 255-.44 2522.<5 2433.#1 245#.51 2413.5 2#3#.45 2#43.12#12.-1 22--.02241.24 2205.22 213.<< 21#2.55

R.Mn km 0.00 31.- 3<.-< <-.-0 105.43 11#.14 120. 123.05 1#5.#2 142.4 14<.415.# 1#.12 1<.- 1-.2132. 133.<# 1<5.0201.0< 20.<< 212.-213.4# 22#.<22<.#< 2#4.-0 2#<.3< 244.< 24<.34 254.1 25<.2 2#.30 23.22 2-2.54 2-.-4 230.34 234.3#


7 mm 450.000 444.000 4#3.000 4#2.000 42.000 420.000 414.000 403.000 402.000 #<.000 #<0.000 #34.000 #-3.000 #-2.000 #.000 #0.000 #54.000 #43.000 #42.000 ##.000 ##0.000 #24.000 #13.000 #12.000 #0.000 #00.000 2<4.000 233.000 232.000 2-.000 2-0.000 24.000 253.000 252.000 24.000 240.000 2#4.000



!1

0.000-# 0.000-3 0.00034 0.0003< 0.000<4 0.00100 0.0010 0.00112 0.00113 0.00124 0.001#1 0.001#3 0.00144 0.00152 0.0015< 0.0010.001-5 0.0013# 0.001<1 0.00200 0.0020< 0.0021< 0.00223 0.002#3 0.0024< 0.0020 0.002-1 0.0023# 0.002< 0.00#0< 0.00#22 0.00## 0.00#51 0.00#0.00#3# 0.00400 0.00413



!2

0.0001# 0.0000< 0.00005 0.00001 0.0000# 0.00000.00012 0.0001 0.00021 0.0002 0.000#1 0.000# 0.00041 0.00040.00052 0.00053 0.0004 0.000-1 0.000-0.00034 0.000<1 0.000<3 0.0010 0.0011# 0.00122 0.001#0 0.001#< 0.00143 0.00150.0010.001-3 0.0013< 0.00200 0.00212 0.00224 0.002#3 0.00251



!#

0.00100 0.000<0.000<5 0.000<2 0.0003< 0.0003 0.0003# 0.000-< 0.000- 0.000-# 0.000< 0.000 0.0002 0.00053 0.00054 0.00050 0.0004 0.00041 0.000#0.000#2 0.00020.00022 0.00010.00012 0.0000 0.00000 0.0000 0.0001# 0.0001< 0.0002 0.000## 0.00041 0.0004< 0.00050.000 0.000-5 0.00035



!4

0.00130.00135 0.00134 0.00132 0.00130 0.001-< 0.001-0.001-5 0.001-# 0.001-1 0.001< 0.0010.0015 0.001# 0.0011 0.00153 0.0015 0.0015# 0.00151 0.00143 0.00145 0.0014# 0.00140 0.001#0.001## 0.001#0 0.00120.0012# 0.0011< 0.00115 0.00111 0.00100.00102 0.000<3 0.000<# 0.00033 0.00032



!5

0.002-# 0.002-# 0.002-# 0.002-2 0.002-2 0.002-1 0.002-1 0.002-1 0.002-0 0.002-0 0.002< 0.002< 0.0023 0.0023 0.0020.0020.002 0.002 0.0025 0.0024 0.0024 0.002# 0.0022 0.0022 0.0021 0.0020 0.0025< 0.00253 0.00250.00250.0025 0.00255 0.0025# 0.00252 0.00251 0.00250 0.0024<



!1

MPa 14.15.-51-.12# 1--.--3 133.-#2 200.000 211.5<4 22#.52< 2#5.321 243.435 21.5#3 2-5.000 233.33< #0#.22 #13.0## ###.### #4<.15# #5.51#32.45 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000



!2

MPa 2.13.<1< 10.<5< 2.--3 5.#4 14.23 2#.133 #2.#5# 41.-<1 51.515 1.5#3 -1.3-5 32.540 <#.543 104.<13 11.123.314 141.#-< 154.#3 1-.35131.313 1<.2< 211.#21 22.<2# 24#.1#20.000 2--.551 2<5.3## #14.3<4 ##4.-3# #55.55 #--.2-# 400.000 400.000 400.000 400.000 400.000



!#

MPa 200.000 1<4.5<5 13<.041 13#.### 1--.45 1-1.42< 15.21153.324 152.2#< 145.455 1#3.42 1#1.250 12#.310 11.12< 103.1<100.000 <1.525 32.-5< -#.34 4.23 54.545 44.444 ##.<2 2#.0-11.-5 0.000 12.245 25.000 #3.2<3 52.1-4 .31.313 <-.-4 114.23 1#1.-0150.000 1<.2#1



!4

MPa #-#.# #-0.# #-.1 ##.< #0. #5-.1 #5#. #50.0 #4.# #42.4 ##3.5 ##4.4 ##0.2 #25.3 #21.# #1.#11.< #0.< #01.3 2<.4 2<0.< 235.2 2-<.2 2-#.1 2.20.0 25#.1 245.3 2#3.# 2#0.4 222.2 21#. 204.1<5.2 135.4 1-5.0 14.1



!5

MPa 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0



!1

k 11-.<5 12.0-1 1#4.40< 142.<-151.-33 10.350 1-0.1-4 1-<.--# 13<.53 1<<.34# 210.#42 221.13 2#2.##3 24#.3< 255.--23.03# 230.305 2<#.< #0-.53< #21.<< #21.<< #21.<< #21.<< #21.<< #21.<< #21.<< #21.<< #21.<< #21.<< #21.<< #21.<< #21.<< #21.<< #21.<< #21.<< #21.<< #21.<<



!2

k 10.-2# -.03 4.401.112.25 5.-45 <.#25 1#.010 1.305 20.-15 24.-4 23.<0# ##.1<1 #-.13 42.1<0 4.<14 51.-<< 5.352 2.032 -.4<< -#.11# -3.<#5 34.<-<1.251 <-.--1 104.552 111.10 113.<2 12.2 1#4.24 142.<-151.-10 10.350 10.350 10.350 10.350 10.350



!#

k 30.425 -3.251 -.013 -#.-2# -1.## 3.<# .4#3 #.31.21< 53.4<1 55.-< 52.--< 4<.-34.<3 4#.503 40.212 #.305 ##.2-< 2<.#0 25.351 21.<#4 1-.3-2 1#.5<.230 4.-#1 0.000 4.<24 10.05# 15.400 20.<30 2.303 #2.<01 #<.2-45.<552.<# 0.#1< 3.052



!4

k 150.12 143.3<5 14-.2< 14.#23 144.<<1 14#.1 142.200 140.-4# 1#<.24# 1#-.<1#.10# 1#4.40 1#2.-5 1#1.015 12<.2012-.##< 125.403 12#.410 121.#4# 11<.201 11.<31 114.30 112.2<1 10<.311 10-.2## 104.552 101.-2 <3.355 <5.325 <2.# 3<.#1 35.<03 32.2<5 -3.510 -4.540 -0.#-2 5.<<0




!5

k 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350

9

!

k 2.303 40.212 5#.<34 3.1#3 32.<0 <-.5< 11#.01 123.<1 145.245 12.03 1-<.40< 1<-.2<2 215.-4# 2#4.-33 254.45< 2-4.-35 2<5.300 #1-.5#< #40.042 ##.#43 #-2.3-3 #32.-2 #<#.01< 40#.-0 414.-40 42.251 4#3.2## 450.-14 4#.-2 4--.#04 4<1.435 50.#10 521.32 523.50 5#5.511 542.3550.00

M

!1

kmm #03.5 #2--3.5# #4<4.22 #-1-4.12 #<44.-3 41320.33 44245.23 4-40.<< 4<#11.1< 51<5<.23 5433.34 5-50#.-1 040-.<4 #405.35 502.0 <-01.4-#00<.#4 -4#1.2-<<-#.2 3#41.- 3#41.- 3#41.- 3#41.- 3#41.- 3#41.- 3#41.- 3#41.- 3#41.- 3#41.- 3#41.- 3#41.- 3#41.- 3#41.- 3#41.- 3#41.- 3#41.- 3#41.-

M

!2

kmm 1#<4.0# <3<.01 5-2.3< 145.21 2<4.51 -4.30 1212.20 1<1.2< 2134.2<#.01 #21.<< #-5-.#4 4#14.35 43<0.#5 5434.-1 0<3.33 -##.3-#<0.- 30-0.-0 3--4.<2 <504.-5 1021.1 1104-.0# 1132.5 12-10.21#5<1.-< 1450<.2< 1545.01 141.41 1-501.1# 1353-.0 1<-22.#5 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44

M

!#

kmm 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

M

!4

kmm 1<51.41 1<#5.2< 1<1<1.-1<022.< 13343.35 13-0.04 1343.04 132<.4 13101.53 1-<00.0 1-<#.45 1-4-<.32 1-25<.41 1-0#1.3< 1-<.<1 1554.10 1#0#.0 104#.# 15--4.54 154<.1# 1520-.5< 14<03.#145<-.35 142-5.40 1#<40.2< 1#5<1.-< 1#22<.05 12351.21 1245-.23 1204.2# 111.<1 1113.03 10<3.#1020.2< <<0.20 <143.#2 35-3.4

M

!5

kmm 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33

M

!

kmm <011.<1 <2<.< <5#35.<3 <-3-2.43 10042<.02 10#053.0 105-4.40 10354<.-< 111413.#2 114#-#.-11-420.112051.- 12#30#.0< 12-143.<1#004.5 1#41-5.## 1#-3-.14 1413.2 145#<.#< 14<-##.< 1501-4.<3 150#2.2 15110-.52 15100.-0 15211#.21 1524.22 15#200.<3 15#--3.3154#31.#4 155010.01 155.1 15#5#.015-0-1.45 155-<.#150#.2< 155521.40 154<51.-#

a mm #32.50 #--.40 #-2.#0 #-.20 #2.10 #5-.00 #51.<0 #4.30 #41.-0 ##.0 ##1.50 #2.40 #21.#0 #1.20 #11.10 #0.00 #00.<0 2<5.30 2<0.-0 235.0 230.50 2-5.40 2-0.#0 25.20 20.10 255.00 24<.<0 244.30 2#<.-0 2#4.0 22<.50 224.40 21<.#0 214.20 20<.10 204.00 1<3.<0


9

7

k #251.25 #20-.<0 #14.55 #121.20 #0--.35 #0#4.50 2<<1.15 2<4-.30 2<04.45 231.10 231-.-5 2--4.40 2-#1.05 23-.-0 244.#5 201.00 255-.5 2514.#0 24-0.<5 242-.0 2#34.25 2#40.<0 22<-.55 2254.20 2210.35 21-.50 2124.15 2030.30 20#-.45 1<<4.10 1<50.-5 1<0-.40 134.05 1320.-0 1---.#5 1-#4.00 1<0.5

M

7

kmm #5#5-#.44 #5-0#<.2#0234.02 ###0-.3 #110.2 #3<1.-5 #-1052.1 #-#1<1.43 #-510<.-2 #-30.3#-3232.<4 #-<5#-.<2 #305-1.32 #31#34.# #31<-.# #32#4-.00 #324<.5 #32425.0# #321#2.42 #3113.-2 #3033#.<4 #-<<23.0#-3-51.12 #--#5#.03 #-5-##.< #-#3<#.-5 #-13#2.4 #<550.03 #-04.2 #4#22.0#1#-.44 #5320<.-2 #54321.<2 #5121#.0# #4-#3#.0 #4###2.00 ##<05<.3

Pn

Mn

k #224.44 #1-.< #110.5#05#.0 2<<5.1 2<#.34 23-3.0< 2313.33 2-5<.21 2<<.0# 2#3.#4 25--.11 2515.#1 2452.<1 2#3<.3< 2#2.22 221.35 21<.- 21#0.<1 204.25 2011.#1<53.14 1<04.5# 1350.5# 1-<.11 1-41.25 135.<2 1#0.0< 15-#.-2 151.30 145<.21401.0< 1#42.22 12<2.1< 1241.34 11<1.1# 1140.05

km 444.1< 450.01 455.41.13 4.54 4-1.-5 4-.32 431.-4 43.5# 4<1.13 4<5.-0 500.10 504.#503.5# 512.53 51.52 520.# 524.11 52-.-5#1.#5 5#1.0 5#0.5 52<.3 523.<5 52-.35 52.54 525.0# 52#.## 521.4# 51<.## 51-.04 514.5 511.3< 50-.-< 50#.45 4<3.35 4<4.01

R.Pn

R 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

k 20<5.3< 205<.00 2021.31<34.4< 1<4.35 1<03.<5 13-0.- 13#2.21-<#.43 1-54.#1-14.<2 1-5.12 1#4.<5 15<4.#< 155#.4# 1512.04 14-0.20 142-.3< 1#35.0< 1#41.- 1#0-.#< 12-2.-< 12#-.<5 1202.34 11-.411#1.31 10<5.35 105<.5 1022.<2 <35.<2 <43.52 <10.-1 3-2.45 3#<.<# 30-.20 --4.24 -41.0#

R.Mn km 233.-2 2<2.50 2<.1< 2<<.-#0#.25 #0.4 #0<.<# #1#.1# #1.24 #1<.2#22.21 #25.0 #2-.34 ##0.55 ###.13 ##5.-4 ##3.24 #40.#4#.05 #45.#3 #45.1< #44.3 #44.41 #4#.32 #4#.10 #42.25 #41.2#40.1 ##3.<# ##-.5##.03 ##4.4##2.-# ##0.0#2-.24 #24.25 #21.11


7 mm 223.000 222.000 21.000 210.000 204.000 1<3.000 1<2.000 13.000 130.000 1-4.000 13.000 12.000 15.000 150.000 144.000 1#3.000 1#2.000 12.000 120.000 114.000 103.000 102.000 <.000 <0.000 34.000 -3.000 -2.000 .000 0.000 54.000 43.000 3.000



!1

0.004#0.00450.004-3 0.00500 0.00524 0.00543 0.005-5 0.000# 0.00## 0.00 0.00-00  0.00-# 0.00-- 0.00320 0.0030.00<10.00<-# 0.010## 0.01100 0.011-4 0.0125 0.01#40.01450 0.0150.01-00 0.01354 0.020## 0.02245 0.02500 0.02311 0.0#200 0.021-1



!2

0.002 0.00231 0.002<0.00#14 0.00##2 0.00#52 0.00#-2 0.00#<4 0.00410.00441 0.0043  0.004<  0.0052 0.0050 0.005< 0.00#5 0.00-0.00-24 0.00--5 0.003#2 0.003<4 0.00<5 0.01044 0.011## 0.012# 0.01#54 0.014<2 0.0155 0.01350 0.0203< 0.02#33 0.015<-



!#

0.000<5 0.00105 0.00110.0012< 0.00141 0.00155 0.001< 0.00134 0.00200 0.00210.002# 0.0025 0.002-0.00#00 0.00#25 0.00#52 0.00#32 0.00414 0.00450 0.0043< 0.005## 0.00532 0.00#3 0.00-00 0.00--1 0.00354 0.00<50 0.0104 0.01200 0.01#0.015-5 0.01024



!4

0.000- 0.000-0 0.0004 0.00050.00050 0.00042 0.000#4 0.0002 0.00010.00000.00004 0.00015 0.00020.00040 0.00054 0.000-0 0.0003 0.00105 0.00125 0.00140.001-2 0.00200 0.002#1 0.0020.00#00.00#54 0.00403 0.004-# 0.00550 0.0044 0.00-# 0.00450

KONDISI TEKAN AKSIAL KECIL 5 Pn 6 7." 8 9:/ 8 b 8 3 KONDISI BALANCE



!5

0.00240.0024 0.00244 0.0024# 0.00241 0.002#< 0.002#3 0.002#5 0.002## 0.002#1 0.0022< 0.0022 0.0022# 0.00220 0.00210.0021# 0.0020< 0.00205 0.00200 0.001<5 0.0013< 0.00132 0.001-5 0.0010.00150.0014 0.001## 0.00113 0.00100 0.000-3 0.00050 0.00124



!1

MPa 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000



!2

MPa 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000



!#

MPa 13<.4-4 210.311 2##.### 25-.14# 232.#5# #0<.0<1 ##-.500 #-.-42 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000



!4

MPa 152. 140.5 12-.3 114.# 100.0 34.3 3.3 51. ##.# 1#.3 -.1 2<. 5#.3 30.0 103.# 1#<.1 1-2.20<.5 250.0 2<4.#44.4 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0



!5

MPa 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 #3<.5 #--.3 #4.#50.0 ###.# #14.# 2<2.# 2.2#.4 200.0 155. 100.0 24-.1



!1

k #21.<< #21.<< #21.<< #21.<< #21.<< #21.<< #21.<< #21.<< #21.<< #21.<< #21.<< #21.<< #21.<< #21.<< #21.<< #21.<< #21.<< #21.<< #21.<< #21.<< #21.<< #21.<< #21.<< #21.<< #21.<< #21.<< #21.<< #21.<< #21.<< #21.<< #21.<< #21.<<



!2

k 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350



!#

k -.1<2 34.--2 <#.32< 10#.40# 11#.541 124.2<# 1#5.-114-.3-3 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350



!4

k 1.#-5.515 51.#32 45.<540.212 #4.120 2-.4 20.-55 1#.404 5.542.3-2 11.<15 21.5# #2.1-0 4#.5# 55.<43 <.453 34.255 100.5#1 113.521 1#3.50< 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350




!5

k 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 10.350 15.1151.<1# 14.5140.-4# 1#4.041 12.#32 11-.544 10-.2## <5.0430.425 2.55# 40.212 <<.#43

9

!

k 553.-41 5-.#21 5-.#-3 535.<52 5<.03< 0.341 13.25 #0.42 4#.#<3 4#.#<3 4#.#<3 4#.#<3 4#.#<3 4#.#<3 4#.#<3 4#.#<3 4#.#<3 4#.#<3 4#.#<3 4#.#<3 4#.#<3 4#.#<3 4#.#<3 4#.#<3 4#.#<3 4#.#<3 4#.#<3 4#.#<3 4#.#<3 4#.#<3 4#.#<3 4#.#<3

M

!1

kmm 3#41.- 3#41.- 3#41.- 3#41.- 3#41.- 3#41.- 3#41.- 3#41.- 3#41.- 3#41.- 3#41.- 3#41.- 3#41.- 3#41.- 3#41.- 3#41.- 3#41.- 3#41.- 3#41.- 3#41.- 3#41.- 3#41.- 3#41.- 3#41.- 3#41.- 3#41.- 3#41.- 3#41.- 3#41.- 3#41.- 3#41.- 3#41.-

M

!2

kmm 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44

M

!#

kmm 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

M

!4

kmm -<-3.<3 -#4.<1 -<.-2 5<-4.41 522-.1 44#5.55 #5<#.<3 2<3.12 1-42.54 -21.05 #-#.40 1543.<2 2314.34132.0< 5#.24 -2-#.20 <02<.51 10<5#.0< 1#0<.0# 1540-.< 1300.21 20<10.44 20<10.44 20<10.44 20<10.44  20<10.44  20<10.44 20<10.44 20<10.44  20<10.44  20<10.44 20<10.44

M

!5

kmm 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 40-20.## #<4<-.50 #31#0.30 #5<#.2#4350.-# #235<.2 #051.41 2-330.5< 24-12.#4 20<10.44 12#.3 10455.22 253#0.54

M

!

kmm 154#52.015#-20.00 15#052.31 152#4-.50 15100.-0 150303.# 14<<-.014<0-1.21 143115.2 14-0<4.1# 145<<<.3 144324.1 14#553.22 1421<1.00 140-0<.34 1#<0<<.3< 1#-#4#.53 1#5420.00 1###04.0 12<34.34 1204#.4< 121--2.51202#5.0# 1134<2.50 11501.0# 11420#.13 111522.#5 103#54.10 104552.20 <<<05.44 <40<.<3 10<4-2.#1

a mm 1<#.30 133.-0 13#.0 1-3.50 1-#.40 13.#0 1#.20 153.10 15#.00 14-.<0 142.30 1#-.-0 1#2.0 12-.50 122.40 11-.#0 112.20 10-.10 102.00 <.<0 <1.30 3.-0 31.0 -.50 -1.40 .#0 1.20 5.10 51.00 45.<0 40.30 5-.30


9

7

k 14-.#0 10#.<5 150.0 151-.25 14-#.<0 14#0.55 1#3-.20 1#4#.35 1#00.50 125-.15 121#.30 11-0.45 112-.10 103#.-5 1040.40 <<-.05 <5#.-0 <10.#5 3-.00 32#.5 -30.#0 -#.<5 <#.0 50.25 0.<0 5#.55 520.20 4-.35 4##.50 #<0.15 #4.30 4<1.#0

M

7

kmm ##45.# #2<352.#2 #24<1.<2 #1<-0.44 #14#32.3#03-34.22 #02<4.43 2<<2#. 2<01.-5 2341-3.- 2--4-4.3 2-054<.52 2#40#.2250#5.<4 24344-.52 240#3.02 2#20-.4# 224#55.- 21533#.00 20-13<.1 1<32-4.2# 13<1#3.22 1-<-31.12 1-0202.<4 1040#.150#3#.#2 140141.33 12<-<.# 113<<5.-5 1030<1.0 <<5.23 1##1<1.4#

Pn

Mn

k 1033.5 10#.# <34.22 <#1.#0 3--.31 32#.-1 -3.<# -1#.42 5-.10 1#.-5 5-0.40 52-.05 43#.-0 440.#5 #<-.00 #5#.5 #10.#0 2.<5 22#.0 130.25 1#.<0 <#.55 50.20 .35 #.50 -<.35 12#.20 1.55 20<.<0 25#.25 2<.0 152.10

km 433.<2 43#.54--.<4-2.11 45.<3 45<.5< 452.<# 445.<< 4#3.-3 4#1.242#.4415.#40.< #<3.2# #3<.1 #-<.-4 #<.<5 #5<.-3 #4<.1< ##-.05 #24.#2 #10.<1 #00.02 233.-0 2-.<0 24.5< 251. 2#3.0# 22#.55 203.00 1<1.0 242.

R.Pn

R 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0. 0.0.3 0.< 0.-0 0.-1 0.-2 0.-# 0.-4 0.-5 0.-0.-3 0.-< 0.30 0.31 0.32 0.3# 0.34 0.35 0.3 0.30.34

R.Mn

k -0-.5 -#.31 #<.-4 05.#4 5-0.53 5#5.41 4<<.31 4#.-# 42-.12 #<3.<4 #-4.<3 #52.20 #23.4#0#.30 2-3.20 251.5 224.11<5.-5 1.#3 1#.03 104.34 -2.5 #<.5# 5.42<.5# 5.4102.#5 140.11-3.<# 213.# 25<.212-.4 #<0.00 #<0.00 0.00

km #1-.30 #14.#2 #10.3 #0.3#02.3< 2<3.-4 2<4.41 23<.<0 235.21 230.## 2-3.#< 2--.52-.# 2-4.-4 2-2.-0 2-0.22 2-.2 2#.31 25<.3# 254.45 243.#5 241.4 2#.25 2#0.4 224.05 21.<5 20<.03 200.#4 1<0.51-<.51-.02 20#.#

0.00 50.00 0.00




7

!1



!2



!#



!4



!5

mm ##

0.00200

0.00034

0.000#2 0.00-#2#5# 0.024<-0



!1

MPa 400.000



!2

MPa 1-.35-



!#

MPa 4.23



!4



MPa

MPa



!5

400

400

!1

k #21.<<







k -.4<<

k 25.351

k 10.350

!2

!#

!4




!5

k 10.350

9

!

k ##.#43

M

!1

kmm 3#41.-

M

!2

kmm 3--4.<2

M

!#

M

!4

kmm kmm 0.00 20<10.440-

M

!5

kmm 41320.33

M

!

kmm 155143.00

a mm 235.0


9

7

k 242-.0

M

7

kmm #3113.-2

Pn

Mn

k 204.25

km 5#.--

R.Pn

R 0.5

k 1#41.-

R.Mn km #43.<0

ANALISIS KEKUATAN KOLOM BETON B DENGAN DIAGRAM INTERAKSI KOLOM GIS ";7 K< KEMBANGAN II

K6 K6)6M

kolom lantai 1

INPUT DATA KOLOM

 78 =  y = b= h= /! = n= =




! = 2.@05 MPa untuk 78 ≤ #0 MPa untuk 7 8 A #0 MPa N1 = 0.35 aktor /i!tribu!i tegangan, %! = n ? π * 4 ? 2 = 4021 mm2 )ua! tulangan total, x =  h  2?/!  * 2 = 1#0.000 mm >arak antara tulangan, 'a!io tulangan, ρ = %! * %g = 1.3 aktor re/uk!i kekuatan, &ntuk " 0 ≤ Pn ≤ 0.1 ?  78 φ = 0.5 untuk Pn O 0.1 ? 78 ? b ? h φ = 0.5 @ 0.15 ?  Pno  φ = 0.30 untuk Pn = 0 Mo/ulu! ela!ti! baja, N1 = 0.35 N1 = 0.35  0.003  78  #0

N2


/1 = 4?x @ /! = 140- mm2 50 mm /2 = #x @ /! = 402 mm2 4#0 mm /2 = 2x @ /! = 402 mm2 #00 mm /2 = x @ /! = 402 mm2 1-0 mm /# = /! = 140- mm2 40 mm 4021 mm2 Pa/a kon/i!i gari! netral terletak pa/a jarak 7 /ari !i!i beton tekan terluar " !i = 0.00# ?  7  / i  * 7 'egangan pa/a ma!ingma!ing baja tulangan " Tegangan pa/a ma!ingma!ing baja tulangan " Q !i Q +  y * ! maka "  !i = ε!i? ! &ntuk Q !i Q ≥  y * ! maka "  !i =Q !i Q * ε!i?  y &ntuk 1 2 # 4 5

%!1 = -*20 ? %! = %!2 = 2*20 ? %! = %!2 = 2*20 ? %! = %!2 = 2*20 ? %! = %!# = -*20 ? %! = %! =


>umlah interal jarak gr URAIAN PERHITUNGAN

PERSAMAAN

Iayagaya internal pa/a ma!ingma!ing baja tulangan " 'e!ultan gaya internal baja tulangan " Momen akibat gaya internal ma!ingma!ing baja tulangan " Momen total akibat gaya internal baja tulangan " Tinggi blok tegangan tekan beton, Iaya internal pa/a beton tekan " Momen akibat gaya internal tekan beton " Iaya ak!ial nominal " Momen nominal " Iaya ak!ial ren7ana " Momen ren7ana "       7

!i = %!i ?  !i ? 1 9! = B Σ !i E?1 M!i = !i?h*2 M! = Σ M!i a = N1 ? 7 97 = 0.35 ?  78 M7 = 97 ? h  Pn = 9! @ 97 Mn = M7 @ M! Pu = φ Pn Mu = φ Mn

!1

!2

!#

!4

!5

mm

!1



!2



!#



MPa

MPa

MPa

MPa

!4


0.000 54.000 43.000 42.000 #.000 #0.000 24.000 13.000 12.000 0.000 00.000 5<4.000 533.000 532.000 5-.000 5-0.000 54.000 553.000 552.000 54.000 540.000 5#4.000 523.000 522.000 51.000 510.000 504.000 4<3.000 4<2.000 43.000 430.000 4-4.000 43.000 42.000 45.000

0.00045 0.0004# 0.00041 0.000#3 0.000# 0.000## 0.000#1 0.00023 0.00025 0.0002# 0.00020 0.00010.00014 0.00011 0.00003 0.00005 0.00002 0.00001 0.00004  0.00003 0.00011  0.00015  0.00013  0.00022  0.0002 0.0002< 0.000## 0.000#0.00041 0.0004  0.00050  0.00054  0.0005<  0.0004  0.0003

0.00105 0.0010# 0.00101 0.000<< 0.000<0.000<5 0.000<# 0.000<1 0.0003< 0.00030.00035 0.0003# 0.00031 0.000-3 0.000- 0.000-4 0.000-1 0.000< 0.000 0.0004 0.0001 0.00053 0.0005 0.0005# 0.00050 0.00040.00044 0.00041 0.000#3 0.000#5 0.000#1 0.00023 0.00024 0.00021 0.0001-

0.0014 0.0012 0.0011 0.0010 0.00153 0.00150.0015 0.00154 0.0015# 0.00151 0.00150 0.00143 0.00140.00145 0.00144 0.00142 0.00140 0.001#< 0.001#0.001#5 0.001## 0.001#1 0.001#0 0.00123 0.0012 0.00124 0.00121 0.0011< 0.00110.00115 0 .0011# 0 .00110 0.00103 0.00105 0.0010#

0.0022# 0.00222 0.00221 0.00221 0.00220 0.0021< 0.00213 0.00210.00210.0021 0.00215 0.00214 0.0021# 0.00212 0.00211 0.00211 0.00210 0.0020< 0.00203 0.00200.0020 0.00204 0.0020# 0.00202 0.00201 0.00200 0.001<< 0.001<3 0.001< 0.001<5 0.001<4 0.001<2 0.001<1 0.001<0 0.00133

0.00232 0.00232 0.00231 0.00231 0.00231 0.00231 0.00231 0.00231 0.00230 0.00230 0.00230 0.00230 0.00230 0.002-< 0.002-< 0.002-< 0.002-< 0.002-3 0.002-3 0.002-3 0.002-3 0.002-3 0.002-0.002-0.002-0.002- 0.002- 0.002- 0.002- 0.002-5 0.002-5 0.002-5 0.002-4 0.002-4 0.002-4

<0.<0< 3.2#< 31.431 -.# -1.<3 .1.5#3 5.#11 50.<30 45.545 40.000 #4.#4# 23.5-1 22.30 1.10.52 4.255 2.151 3.< 15.#35 22.222 2<.21# #.#4 4#.-3 51.1# 53.324 .-4.<< 32.<2<1.#53 100.000 103.31 11-.<4< 12-.2-# 1#.342

20<.0<1 205.505 201.352 1<3.1#1 1<4.#40 1<0.4- 13.5#3 132.524 1-3.4#1 1-4.251-0.000 15.511.224 15.-01 152.03# 14-.#3 142.55# 1#-.#4 1#2.0< 12-.4-# 122.222 11.354 111.#4 105.-4100.000 <4.113 33.0<5 31.<23 -5.10 <.1# 2.500 55.< 43.-13 41.553 #4.211

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P no = 52<3 k

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netral =

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0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

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φ.Πν (κΝ)

450 400 #50 #00 250 200 150 100 50 0 0

2

4

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3

10 12 14 1

ANALISIS KOLOM DENG

4000 #300 #00 #400 #200 #000 2300 200 2400 2200

φ.Πν (κΝ)

2000

1300 100 1400 1200 1000 300 00 400 200 0 0

20

40

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ANALISIS KOLOM DENG M

M

M

a

9

M

kmm

kmm

kmm

mm

k

kmm

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Pn

Mn

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1<51.41 1<#5.2< 1<1<1.-1<022.< 13343.35 13-0.04 1343.04 132<.4 13101.53 1-<00.0 1-<#.45 1-4-<.32 1-25<.41 1-0#1.3< 1-<.<1 1554.10 1#0#.0 104#.# 15--4.54 154<.1# 1520-.5< 14<03.#145<-.35 142-5.40 1#<40.2< 1#5<1.-< 1#22<.05 12351.21 1245-.23 1204.2# 111.<1 1113.03 10<3.#1020.2< <<0.20 <143.#2 35-3.4 -<-3.<3 -#4.<1 -<.-2 5<-4.41 522-.1 44#5.55 #5<#.<3 2<3.12 1-42.54 -21.05 #-#.40 1543.<2 2314.34132.0< 5#.24 -2-#.20 <02<.51 10<5#.0< 1#0<.0# 1540-.< 1300.21 20<10.44 20<10.44 20<10.44

41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 40-20.## #<4<-.50 #31#0.30 #5<#.2#4350.-#

11#1#.#< 11-550.5< 1215<5.4 125-5#.01#002-.0 1#4424.2 1#3<43.# 14#05.5# 143401.-1 15##4#.2# 1534#.30 1#3<.54 1<10<.04 1-4-0#.# 130431.10 13451.4# 1<224.14 1<<00<.-1 2051<.## 21245.01 212<0.#1 21###.<4 21#3#3.35 214##2.02 214344.5# 215#--.54 215<#2.#1 21510.1< 21-112. 21--41.## 213#<-.<4 21<034.#< 21<302.-21<#10.< 213-<4.1 213252.-2 21-3#.05 21-03#.#< 21451.#2 215-34.1# 2150-3.32 214##2.02 21#5#<.< 212<3.#< 211302.5# 21034.<4 20<325.4 203-#1.01 20-555.4< 2023<.54 204<22.#2 20#441.1 2013#1.21 2000-4.<0 1<3151.#2 1<0#5.#3 1<25<.1 133--4.31 13450#.3< 132<.# 13122#.32

#32.50 #--.40 #-2.#0 #-.20 #2.10 #5-.00 #51.<0 #4.30 #41.-0 ##.0 ##1.50 #2.40 #21.#0 #1.20 #11.10 #0.00 #00.<0 2<5.30 2<0.-0 235.0 230.50 2-5.40 2-0.#0 25.20 20.10 255.00 24<.<0 244.30 2#<.-0 2#4.0 22<.50 224.40 21<.#0 214.20 20<.10 204.00 1<3.<0 1<#.30 133.-0 13#.0 1-3.50 1-#.40 13.#0 1#.20 153.10 15#.00 14-.<0 142.30 1#-.-0 1#2.0 12-.50 122.40 11-.#0 112.20 10-.10 102.00 <.<0 <1.30 3.-0 31.0 -.50

#251.25 #20-.<0 #14.55 #121.20 #0--.35 #0#4.50 2<<1.15 2<4-.30 2<04.45 231.10 231-.-5 2--4.40 2-#1.05 23-.-0 244.#5 201.00 255-.5 2514.#0 24-0.<5 242-.0 2#34.25 2#40.<0 22<-.55 2254.20 2210.35 21-.50 2124.15 2030.30 20#-.45 1<<4.10 1<50.-5 1<0-.40 134.05 1320.-0 1---.#5 1-#4.00 1<0.5 14-.#0 10#.<5 150.0 151-.25 14-#.<0 14#0.55 1#3-.20 1#4#.35 1#00.50 125-.15 121#.30 11-0.45 112-.10 103#.-5 1040.40 <<-.05 <5#.-0 <10.#5 3-.00 32#.5 -30.#0 -#.<5 <#.0 50.25

#5#5-#.44 #5-0#<.2#0234.02 ###0-.3 #110.2 #3<1.-5 #-1052.1 #-#1<1.43 #-510<.-2 #-30.3#-3232.<4 #-<5#-.<2 #305-1.32 #31#34.# #31<-.# #32#4-.00 #324<.5 #32425.0# #321#2.42 #3113.-2 #3033#.<4 #-<<23.0#-3-51.12 #--#5#.03 #-5-##.< #-#3<#.-5 #-13#2.4 #<550.03 #-04.2 #4#22.0#1#-.44 #5320<.-2 #54321.<2 #5121#.0# #4-#3#.0 #4###2.00 ##<05<.3 ##45.# #2<352.#2 #24<1.<2 #1<-0.44 #14#32.3#03-34.22 #02<4.43 2<<2#. 2<01.-5 2341-3.- 2--4-4.3 2-054<.52 2#40#.2250#5.<4 24344-.52 240#3.02 2#20-.4# 224#55.- 21533#.00 20-13<.1 1<32-4.2# 13<1#3.22 1-<-31.12 1-0202.<4

#1#5.<#0-#.1# #00<.- 2<45.3# 2331.#2 231.20 2-50.4 234.05 21.< 254<.15 2430.53 2411.2# 2#41.05 22-0.01 21<3.0 2125.15 2051.25 1<-.2< 1<00.22 1322.<3 1--0.10 1-1.3 1#.2 10<.2 1554.34 14<<.<1444.4 1#33.31 1##2.45 12-5.52 121-.<< 115<.32 1100.<5 1050.<2 1000.5 <4<.3 3<3.-3 34-.2< -<5.#5 -42.<5 <0.02 #.54 532.4# 52-. 4-2.15 415.3# #-2.43 #2<.1# 235.-3 242.4# 1<<.03 155.-# 112.#3 <.0# 25.3 1-.1.02 104.#14-.-2 1<1.02#4.42

4-.1< 4-4.5< 431.33 43<.0 4<.14 50#.12 510.00 51.30 52#.51 5#0.15 5#.-2 54#.2# 54<.3 55.0< 52.4 53.30 5-5.12 531.4# 53-.-5 5<4.03 5<#.-< 5<#.2< 5<2.5< 5<1.< 5<0.53 53<.253-.- 53.0 534.1 532.0 5-<.-5--.2< 5-4.2 5-0.52 5.13 51.53 55.-4 551.5 54.#0 540.-0 5#4.34 523.-1 522.#2 515. 503.-# 501.51 4<4.00 43.21 4-3.11 4<.< 40.< 451.3< 442.44#2.3 422.51 411.<2 #<<.-< #3-.05 #-#.4 #2.-5 #51.4#

0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.0.3 0.-0 0.-1 0.-2 0.-# 0.-4 0.-5 0.- 0.-0.-3 0.-< 0.30 0.32 0.3# 0.34 0.35 0.3

20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44 20<10.44

#235<.2 #051.41 2-330.5< 24-12.#4 20<10.44 12#.3 10455.22 253#0.54

1-<2#2.#5 1-<#4.50 1-425#.1-1035.42 1-23#.5# 12#.- 15323.#1 1-220#.#

-1.40 .#0 1.20 5.10 51.00 45.<0 40.30 5-.30

0.<0 5#.55 520.20 4-.35 4##.50 #<0.15 #4.30 4<1.#0

1040#.150#3#.#2 140141.33 12<-<.# 113<<5.-5 1030<1.0 <<5.23 1##1<1.4#

2--.-#21.12 #4.440-.32 451.14<4.52 5#-.3#<#.#-

##<.4 #2-.#2 #14.40 #00.- 23.23 2-0.-# 25#.-< #05.40

0.30.33 0.3< 0.<0 0.<1 0.<2 0.<# 0.<0

20<10.440-

41320.33

21-3-<.#2

235.0

242-.0

#3113.-2

1322.<3

5<<.50

0.5

b= h=

400 00

%7

D

 78 =  y =

25 400

Tul. "

13 20 22 24 2 23 #0 #2 #4 # #3 40 42 44 4 43 50

Pu

Mu

k

km

112.54

2#.#20

12<.-03

21.#14

124.013

2#.33

32.32<

25.<15

1#.043

2.<<#

11.54<

20.454

114.222

#1.#22

-2.350

#4.-3

mm mm "4

MPa MPa

φ.Μν (κΝµ)

N DIAGRAM INTERAKSI

Tul. "

b= h=

400 00

mm mm

%7

D

"4

 78 =

25

MPa

 y =

0 140 10 130 200 220 240 20 230 #00 #20 #40 #0 #30 400

φ.Μν (κΝµ)

N DIAGRAM INTERAKSI R.Pn k #44#.<3 ##22.3< #233.34 #254.< #220.4# #13.0 #151.5 #11.<4 #032.20 #04-.## #012.## 2<--.1< 2<41.<1 2<0.4< 23-0.<1 23#5.1< 2-<<.#0 2-#.25 2-2-.0# 2<0.# 254.0 21-.2< 2530.#4 254#.13 2505.32 243.25 24#0.45 2#<2.4# 2#54.1 2#15. 22-.3< 22#-.3 21<3.5 2153.<211<.0< 20-3.<0

R.Mn km 0.00 -2.4< 31.00 3<.40 <-.105.3# 11#.3 121.-3 12<.53 1#-.2 144.3# 152.23 15<.2 1.35 1-#.< 130.< 13-.35 1<4.4 201.#1 20-.33 214.#4 220.< 22.<5 2##.10 2#<.15 245.10 250.< 25.4 22.22 2-.-1 2-#.11 2-3.42 23#.# 233.-2<#.32 2<3.-3

400

Pu

Mu

k

km

112.54

2#.#20

12<.-03

21.#14

124.013

2#.33

32.32<

25.<15

1#.043

2.<<#

11.54<

20.454

114.222

#1.#22

-2.350

#4.-3

MPa

20#3.#3 1<<-.54 1<5.#4 1<14.-< 13-2.3 13#0.5# 1-3-.30 1-44.4 1-01.02 15.<5 112.#3 15-.#0 1521.3 14-5.51 1423.-4 1#31.#5 1###.#1 1234.5< 12#5.14 1134.<4 1150.5 1115.< 1031.12 104.02 1010.4 <-4.<3 <#<.02 <02.-# 3.0< 32<.0< -<1.< -5#.33 -15.2 3#.10 50.#1-.41 534.20 550.-4 51.<3 432.<2 443.52 41#.-5 #31.14 #52.52 #21.<< 23<.4# 2#.#0 2#.22 203.20 1-<.25 14<.#5 113.52 3.-4 54.0# 20.#3 14.22 4<.-5 3.22 12#.# 11.<< 201.23

#0#.#03.43 #1#.22 #1-.3< #22.4< #2-.0# ##1.50 ##5.<2 #40.23 #44.0 #43.3#5#.10 #5-.2< #1.4 #5.0 #<.-2 #-#.3# #--.<# #32.04 #3.15 #35.< #35.4 #35.13 #34.0 #3#.33 #3#.0# #32.05 #30.<4 #-<.-0 #-3.#4 #-.35 #-5.24 #-#.51 #-0.34 #3.02 #5.0# #1.33 #53.5#55.10 #51.4 #4-.5 #4#. #41.30 #44.51 #4.<# #4<.0#4<.20 #43.< #43.## #4-.2< #45.32 #4#.<2 #41.54 ##3.3 ##5.2< ##1.#5 #25.<# #1<.-4 #12.-1 #0-.5# #01.-4

241.51 232.3 #24.-< #-.34 411.3# 45.- 502.2 #5#.#3

2<5.2< 233.1# 230.1 2-1.23 21.#1 250.05 2#-.1 2-4.#5

#<0.00 #<0.00

0.00 50.00

0.00 1134.<4

0.00 #3<.-

ANALISIS KEKUATAN KOLOM BETO DENGAN DIAGRAM INTERAKSI KOLOM GIS ";7 K< KEMBANGAN II

K6 K6)6M

K6)6M )%T%F 2

INPUT DATA KOLOM

 78 =  y = b= h= /! = n= =


25 MPa 400 MPa 400 mm 00 mm 40 mm 1 buah 1 mm


! = 2.@05 MPa untuk 78 ≤ #0 MPa untuk 7 8 A #0 MPa N1 = 0.35 aktor /i!tribu!i tegangan, %! = n ? π * 4 ? 2 = #21- mm2 )ua! tulangan total, x =  h  2?/!  * 2 = 1#0 mm >arak antara tulangan, 'a!io tulangan, ρ = %! * %g = 1.#4 aktor re/uk!i kekuatan, &ntuk " 0 ≤ Pn ≤ 0.1 ?  78 φ = 0.5 untuk Pn O 0.1 ? 78 ? b ? h φ = 0.5 @ 0.15 ?  Pno  φ = 0.30 untuk Pn = 0 Mo/ulu! ela!ti! baja, N1 = 0.35 N1 = 0.35  0.003  78  #0

N2


/1 = 4?x @ /! = 1005 mm2 50 mm /2 = #x @ /! = 402 mm2 4#0 mm /2 = 2x @ /! = 402 mm2 #00 mm /2 = x @ /! = 402 mm2 1-0 mm /# = /! = 1005 mm2 40 mm #21- mm2 Pa/a kon/i!i gari! netral terletak pa/a jarak 7 /ari !i!i beton tekan terluar " !i = 0.00# ?  7  / i 'egangan pa/a ma!ingma!ing baja tulangan " Tegangan pa/a ma!ingma!ing baja tulangan " Q !i Q +  y * ! maka "  !i = ε!i? ! &ntuk Q !i Q ≥  y * ! maka "  !i =Q !i Q * ε!i?  y &ntuk 1 2 # 4 5

%!1 = 5*1 ? %! = %!2 = 2*1 ? %! = %!2 = 2*1 ? %! = %!2 = 2*1 ? %! = %!# = 5*1 ? %! = %! =



PERSAMAAN


!i = %!i ?  !i ? 9! = B Σ !i E?1 M!i = !i?h*2 M! = Σ M!i a = N1 ? 7 97 = 0.35 ?  78 M7 = 97 ? h  Pn = 9! @ 97 Mn = M7 @ M! Pu = φ ? Pn Mu = φ Mn

!1

!2

!#

!4

!5

mm

!1

MPa



!2



!#



MPa

MPa

MPa

!4


0.000 54.000 43.000 42.000 #.000 #0.000 24.000 13.000 12.000 0.000 00.000 5<4.000 533.000 532.000 5-.000 5-0.000 54.000 553.000 552.000 54.000 540.000 5#4.000 523.000 522.000 51.000 510.000 504.000 4<3.000 4<2.000 43.000 430.000 4-4.000 43.000 42.000 45.000

0.00045 0.0004# 0.00041 0.000#3 0.000# 0.000## 0.000#1 0.00023 0.00025 0.0002# 0.00020 0.00010.00014 0.00011 0.00003 0.00005 0.00002 0.00001 0.00004 0.00003  0.00011 0.00015 0.00013 0.00022 0.0002 0.0002< 0.000## 0.000#0.00041 0.0004 0.00050 0.00054 0.0005< 0.0004 0.0003

0.00105 0.0010# 0.00101 0.000<< 0.000<0.000<5 0.000<# 0.000<1 0.0003< 0.00030.00035 0.0003# 0.00031 0.000-3 0.000- 0.000-4 0.000-1 0.000< 0.000 0.0004 0.0001 0.00053 0.0005 0.0005# 0.00050 0.00040.00044 0.00041 0.000#3 0.000#5 0.000#1 0.00023 0.00024 0.00021 0.0001-

0.0014 0.0012 0.0011 0.0010 0.00153 0.00150.0015 0.00154 0.0015# 0.00151 0.00150 0.00143 0.00140.00145 0.00144 0.00142 0.00140 0.001#< 0.001#0.001#5 0.001## 0.001#1 0.001#0 0.00123 0.0012 0.00124 0.00121 0.0011< 0.00110.00115 0.0011# 0.00110 0.00103 0.00105 0.0010#

0.0022# 0.00222 0.00221 0.00221 0.00220 0.0021< 0.00213 0.00210.00210.0021 0.00215 0.00214 0.0021# 0.00212 0.00211 0.00211 0.00210 0.0020< 0.00203 0.00200.0020 0.00204 0.0020# 0.00202 0.00201 0.00200 0.001<< 0.001<3 0.001< 0.001<5 0.001<4 0.001<2 0.001<1 0.001<0 0.00133

0.00232 0.00232 0.00231 0.00231 0.00231 0.00231 0.00231 0.00231 0.00230 0.00230 0.00230 0.00230 0.00230 0.002-< 0.002-< 0.002-< 0.002-< 0.002-3 0.002-3 0.002-3 0.002-3 0.002-3 0.002-0.002-0.002-0.002- 0.002- 0.002- 0.002- 0.002-5 0.002-5 0.002-5 0.002-4 0.002-4 0.002-4

<0.<0< 3.2#< 31.431 -.# -1.<3 .1.5#3 5.#11 50.<30 45.545 40.000 #4.#4# 23.5-1 22.30 1.10.52 4.255 2.151 3.< 15.#35 22.222 2<.21# #.#4 4#.-3 51.1# 53.324 .-4.<< 32.<2<1.#53 100.000 103.31 11-.<4< 12-.2-# 1#.342

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400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000

400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000

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BERTULANG

?b?h

Pn  * Pno Pa/a kon/i!i tekan ak!ial !entri! Mno = 0 " Pno = 0.30?B 0.35? 78 ?b?h @ %!? y  0.35? 78E →

P no = 5055 k

0.1 ?  78 ? b ? h ?10# =

00

k

Pa/a kon/i!i balan7e " = 7b = 00 * 00 @  y ? /1 = ##.00 mm

*7

netral =

100

→

∆7 = .0000 UNIT

0# 0# /i










MPa

k

k

k

k

k

k

kmm

kmm

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0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

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φ.Πν (κΝ)

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ANALISIS KOLOM DENG

4000 #300 #00 #400 #200 #000 2300 200 2400 2200

φ.Πν (κΝ)

2000

1300 100 1400 1200 1000 300 00 400 200 0 0

20

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Pn

Mn

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41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 41320.33 40-20.## #<4<-.50 #31#0.30 #5<#.2#4350.-#

<32-<.010111.#2 104122.54 10-1.01 1102<5.21 11#51#.32 11325.-2 1202#5.0# 12#-4.12 12-##.5< 1#10<2.#3 1#4<#-.< 1#3<05.014#000.4# 14-2#0.015100.-0 1511<.43 10-<4.03 15#2.-0 1-044.1# 1-1035.42 1-154#.0 1-201-.<1-2511.14 1-#02#.5 1-#55. 1-4111.42 1-43<.#1 1-52<1.-3 1-5<20.45 1-5--.05 1--2#.51 1--<31.3< 1--43<.31 1-<-#.-# 1-4#1.34 1-532.11-522.51 1-4#0.44 1-#<#.25 1-#25-.<4 1-2511.14 1-1-1<.01-03--.51 1<<31.5 1<02.0 13004.53 1<10.12 15-#4.0 1443. 1#101.44 1120.23 10010.## 153254.02 15##0.44 154214.50 150--5.23 14<5#.<# 1423#.01 141145.41#<402.<4

#32.50 #--.40 #-2.#0 #-.20 #2.10 #5-.00 #51.<0 #4.30 #41.-0 ##.0 ##1.50 #2.40 #21.#0 #1.20 #11.10 #0.00 #00.<0 2<5.30 2<0.-0 235.0 230.50 2-5.40 2-0.#0 25.20 20.10 255.00 24<.<0 244.30 2#<.-0 2#4.0 22<.50 224.40 21<.#0 214.20 20<.10 204.00 1<3.<0 1<#.30 133.-0 13#.0 1-3.50 1-#.40 13.#0 1#.20 153.10 15#.00 14-.<0 142.30 1#-.-0 1#2.0 12-.50 122.40 11-.#0 112.20 10-.10 102.00 <.<0 <1.30 3.-0 31.0 -.50

#251.25 #20-.<0 #14.55 #121.20 #0--.35 #0#4.50 2<<1.15 2<4-.30 2<04.45 231.10 231-.-5 2--4.40 2-#1.05 23-.-0 244.#5 201.00 255-.5 2514.#0 24-0.<5 242-.0 2#34.25 2#40.<0 22<-.55 2254.20 2210.35 21-.50 2124.15 2030.30 20#-.45 1<<4.10 1<50.-5 1<0-.40 134.05 1320.-0 1---.#5 1-#4.00 1<0.5 14-.#0 10#.<5 150.0 151-.25 14-#.<0 14#0.55 1#3-.20 1#4#.35 1#00.50 125-.15 121#.30 11-0.45 112-.10 103#.-5 1040.40 <<-.05 <5#.-0 <10.#5 3-.00 32#.5 -30.#0 -#.<5 <#.0 50.25

#5#5-#.44 #5-0#<.2#0234.02 ###0-.3 #110.2 #3<1.-5 #-1052.1 #-#1<1.43 #-510<.-2 #-30.3#-3232.<4 #-<5#-.<2 #305-1.32 #31#34.# #31<-.# #32#4-.00 #324<.5 #32425.0# #321#2.42 #3113.-2 #3033#.<4 #-<<23.0#-3-51.12 #--#5#.03 #-5-##.< #-#3<#.-5 #-13#2.4 #<550.03 #-04.2 #4#22.0#1#-.44 #5320<.-2 #54321.<2 #5121#.0# #4-#3#.0 #4###2.00 ##<05<.3 ##45.# #2<352.#2 #24<1.<2 #1<-0.44 #14#32.3#03-34.22 #02<4.43 2<<2#. 2<01.-5 2341-3.- 2--4-4.3 2-054<.52 2#40#.2250#5.<4 24344-.52 240#3.02 2#20-.4# 224#55.- 21533#.00 20-13<.1 1<32-4.2# 13<1#3.22 1-<-31.12 1-0202.<4

#1<4.<5 #1#.1#0-.< #01-.#2 2<5-.21 23<.# 23#5.55 2--#.<4 2-11.-< 24<.02535.- 2521.32 245-.22 2#<1.<4 2#25.<5 225<.1< 21<1.5 212#.22054.01 1<3#.3# 1<#0.<5 13--.-1 1324.11 1--0.10 1-15.< 10.32 105.4< 154<. 14<#.#0 14#.#1#-3.34 1#20. 121.30 1211.-111.41 1110.-1 105<.2 1003.1# <5.20 <0#.30 350.3-<-.#< -4#.23 33.51 ##.00 5-.3 5##.## 43<.<3 44.# 40#.23 #5<.<# #1.53 2-#.2# 22<.33 13.5# 14#.13 <<.3# 5.43 1#.1# #0.22 -#.5-

451.35 453.20 44.41 4-0.44-.41 432.21 43-.33 4<#.4# 4<3.3 504.150<.#3 514.43 51<.43 524.#< 52<.21 5##.<5 5#3.2 54#.22 54-.-552.2 551.<551.4550.-54<.3 543.- 54-.45 545.<4 544.24 542.#4 540.24 5#-.<5 5#5.45#2.30 523.-0 524.# 51<.- 514.<2 50<.3# 504.43 4<3.33 4<#.02 43.3< 430.50 4-#.34 4.<1 45<.< 452.13 444.#3 4#.23 42-.341<.14 410.0400.5 #<0.3 #30.< #-0.10 #5-.< #45.2# ##1.32 #20.<# #0<.1

0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0. 0.0.3 0.< 0.-0 0.-1 0.-2 0.-# 0.-4 0.-5 0.- 0.-3 0.-< 0.30 0.31 0.32

 2 0 < 1 0 .44  2 0 < 1 0 .44  2 0 < 1 0 .44  2 0 < 1 0 .44  2 0 < 1 0 .44  2 0 < 1 0 .44  2 0 < 1 0 .44  2 0 < 1 0 .44

# 2 3 5 < .2  # 0 5  1 .4 1 2 - 3 3 0 .5 < 2 4 - 1 2 .# 4 2 0 < 1 0 .4 4 1  2  # . 3 1 0 4 5 5 .2 2 2 5 3 # 0 .5 4

1#-411.41#511#.2 1 # 2 4 # 2 .-< 1 2 < 2  4 .54 1 2 5 4  2 .4 1 2 0 3 1 5 .33 11500-.42 1 # 0 # 3 2 .-5

- 1 .4 0   .# 0  1 .2 0 5  .1 0 5 1 .0 0 4 5 .< 0 4 0 .3 0 5 - .3 0

0.<0 5#.55 520.20 4-.35 4##.50 #<0.15 #4.30 4<1.#0

1040#.150#3#.#2 140141.33 12<-<.# 113<<5.-5 1030<1.0 <<5.23 1##1<1.4#

11.<2  1  0 .2  2 0 # . 2  2 4  .<  2 < 0 .# 2  # # # .  # - - .0 2  2 # 2 .5 2

2 < - .3 2 2 3 5 .5 0 2 - 2 .5 2 5 3 .< 4 2 4 4 .4  2 2 3 .< 1 211.<2  # .5 -

0 .3 # 0 .3 4 0 .3 5 0 .3  0 .3 0 .3 3 0 .3 < 0 .3 

2 0 < 1 0 .4 4 0 -

41320.33 41

1 -  0 5 3 .4 4

2 3 5 . 0

242-.0

#3113.-2

1 < 3 # .3 #

5 5 - . 3

0 . 5

b= h=

400 00

"4

D

 78 =  y =

25 400

Tul. "

1 3 2 0 2 2 2 4 2  2 3 #0 # 2 # 4 #  # 3 4 0 4 2 4 4 4 4 3 5 0

Pu

Mu

k

km

112 12.5 .54 4

2#.# 2# .#20 20

12<. 12 <.-0 -033

21.# 21 .#14 14

124. 12 4.01 0133

2#.3 2# .33 3

32. 2.332<

25. 5.<<15

1#. 1 #.04 0433

2.< 2 .<<# <#

11 1.5 .54< 4<

20.4 20 .454 54

114 14.2 .222 22

#1.# #1 .#22 22

-2. 2.3350

#4. 4.-3

mm mm "4

MPa MPa

φ.Μν (κΝµ)

N DIAGRAM INTERAKSI

Tul. "

b= h=

400 00

mm mm

"4

D

"4

 78 =

25

MPa

 y =

0 140 10 130 200 220 240 20 230 #00 #20 #40 #0 #30 400

φ.Μν (κΝµ)

N DIAGRAM INTERAKSI R.Pn k # 2 3 5 . 5< # 2 3 5 . 5< # 2   . #0 # 2 # # . 40 # 2 0 0 . 40 # 1  - . #2 # 1 # 4 . 14 # 1 0 0 . 3 # 0  - . 4< # 0 # 4 . 01 # 0 0 0 . 4# 2 <   . -4 2 < # 2 . <4 2 3 < < . 02 2 3  4 . << 2 3 # 0 . 3# 2 - <  . 55 2 -  2 . 14 2 - 2 - . 5< 2  < 2 . <0 2  5 3 . 03 2  2 # . 10 2 5 3 - . <2 5 5 2 . < 2 5 1 - . 24 2 4 3 1 . 2 2 4 4 5 . 3# 2 4 0 < . 35 2 # - # . < 2 # # - . ## 2 # 0 0 . -2 2  4 . 00 2 2 2 - . 02 2 1 3 < . 30 2 1 5 2 . # 2114.

R.Mn km 0 .0 0 - 3 . 3  .3  < 4 .< 4 1 02 .3 3 110.-0 113.#< 1 25 .<  1 ## .4 1 1 40 .- # 1 4- .< # 1 55 .0 0 1 1 .<  1 3 .- < 1 -5 .5 0 1 32 .0 < 1 33 .5 1 <4 .< 2 2 01 .1  2 0- .2 < 2 1# .2 < 2 1< .1 3 2 24 .<  2 #0 . # 2 # .1 3 2 41 . # 2 4 .<  252.11 2 5- .1 5 2 2 .0 3 2  .< 0 2 -1 . 2 2 - .2 4 2 30 .- 5 2 35 .1 2 3< .4 3

400

MPa

20-.-2 20#3.51 2000.0# 1<1.2 1<22.1< 1332.31 134#.10 130#.0 1-2. 1-21.<0 130.-4 1#<.13 15<-.1< 1554.- 1511.3143.43 1424.51#30.12 1##5.11 123<.4< 1255.12 1220.51 1135.1150.51115.20 10-<.54 104#.5100-.23 <-0.4 <##.4 3<.25 353.4# 320.1-3-.5 -54.<2 -21.< 33.- 55.2< 21.5# 53-.455#.0513.#0 43#.1# 44-.5# 411.45 #-3.20 #55.55 ##1.< #0-.4# 231.< 255.55 223.21 1<<.<2 1-0.< 140.52 10<.42 --.#44.#3 10.4 24.41 0.21

2<#.-0 2<-.3# #01.3 #05.31 #0<. #1#.4# #1-.12 #20.-# #24.2 #2-.-1 ##1.0< ##4.41 ##-. #40.35 #4#.<3 #4-.0#50.10 #5#.0< #5.05 #53.<#53.-3 #53.4 #53.00 #5-.41 #5.< #55.34 #54.3 #5#.- #52.52 #51.1 #4<.#43.0 #4.#2 #4#. #40.3# ##-.35 ##4.-0 ##1.#< #2-.<1 #24.2#20.4 #1.43 #12.## #03.00 #0#.4< #01.43 #01.4 #01.0#00.#1 2<<.1 2<-.0 2<5.0 2<#.15 2<0.2# 23.30 232.3# 2--.44 2-1.#1 24.#25<.125#.#3

<.< 1#4.4 1-#.2 212.3# 25#.## 2<4.-##-.15 1<<.54

24.< 2#<.34 2#1.<4 22#.14 21#.#1 202.22 13<.5 22.13

#<0.00 #<0.00

0.00 50.00

0.00 123<.4<

0.00 #2.4<

ANALISIS KEKUATAN KOLOM BETON B DENGAN DIAGRAM INTERAKSI KOLOM GIS ";7 K< KEMBANGAN II

K6 K6)6M

kolom atap

INPUT DATA KOLOM

 78 =  y = b= h= /! = n= =




! = 2.@05 MPa untuk 78 ≤ #0 MPa untuk 7 8 A #0 MPa N1 = 0.35 aktor /i!tribu!i tegangan, %! = n ? π * 4 ? 2 = 241# mm2 )ua! tulangan total, x =  h  2?/!  * 2 = 1#0.000 mm >arak antara tulangan, 'a!io tulangan, ρ = %! * %g = 1.01 aktor re/uk!i kekuatan, &ntuk " 0 ≤ Pn ≤ 0.1 ?  78 φ = 0.5 untuk Pn O 0.1 ? 78 ? b ? h φ = 0.5 @ 0.15 ?  Pno  φ = 0.30 untuk Pn = 0 Mo/ulu! ela!ti! baja, N1 = 0.35 N1 = 0.35  0.003  78  #0

N2


/1 = 4?x @ /! = 0# mm2 50 mm /2 = #x @ /! = 402 mm2 4#0 mm /2 = 2x @ /! = 402 mm2 #00 mm /2 = x @ /! = 402 mm2 1-0 mm /# = /! = 0# mm2 40 mm 241# mm2 Pa/a kon/i!i gari! netral terletak pa/a jarak 7 /ari !i!i beton tekan terluar " !i = 0.00# ?  7  / i  * 7 'egangan pa/a ma!ingma!ing baja tulangan " Tegangan pa/a ma!ingma!ing baja tulangan " Q !i Q +  y * ! maka "  !i = ε!i? ! &ntuk Q !i Q ≥  y * ! maka "  !i =Q !i Q * ε!i?  y &ntuk 1 2 # 4 5

%!1 = #*12 ? %! = %!2 = 2*12 ? %! = %!2 = 2*12 ? %! = %!2 = 2*12 ? %! = %!# = #*12 ? %! = %! =



PERSAMAAN


!i = %!i ?  !i ? 1 9! = B Σ !i E?1 M!i = !i?h*2 M! = Σ M!i a = N1 ? 7 97 = 0.35 ?  78 M7 = 97 ? h  Pn = 9! @ 97 Mn = M7 @ M! Pu = φ Pn Mu = φ Mn

!1

!2

!#

!4

!5

mm

!1



!2



!#



MPa

MPa

MPa

MPa

!4


0.000 54.000 43.000 42.000 #.000 #0.000 24.000 13.000 12.000 0.000 00.000 5<4.000 533.000 532.000 5-.000 5-0.000 54.000 553.000 552.000 54.000 540.000 5#4.000 523.000 522.000 51.000 510.000 504.000 4<3.000 4<2.000 43.000 430.000 4-4.000 43.000 42.000 45.000

0.00045 0.0004# 0.00041 0.000#3 0.000# 0.000## 0.000#1 0.00023 0.00025 0.0002# 0.00020 0.00010.00014 0.00011 0.00003 0.00005 0.00002 0.00001 0.00004  0.00003 0.00011  0.00015  0.00013  0.00022  0.0002 0.0002< 0.000## 0.000#0.00041 0.0004  0.00050  0.00054  0.0005<  0.0004  0.0003

0.00105 0.0010# 0.00101 0.000<< 0.000<0.000<5 0.000<# 0.000<1 0.0003< 0.00030.00035 0.0003# 0.00031 0.000-3 0.000- 0.000-4 0.000-1 0.000< 0.000 0.0004 0.0001 0.00053 0.0005 0.0005# 0.00050 0.00040.00044 0.00041 0.000#3 0.000#5 0.000#1 0.00023 0.00024 0.00021 0.0001-

0.0014 0.0012 0.0011 0.0010 0.00153 0.00150.0015 0.00154 0.0015# 0.00151 0.00150 0.00143 0.00140.00145 0.00144 0.00142 0.00140 0.001#< 0.001#0.001#5 0.001## 0.001#1 0.001#0 0.00123 0.0012 0.00124 0.00121 0.0011< 0.00110.00115 0 .0011# 0 .00110 0.00103 0.00105 0.0010#

0.0022# 0.00222 0.00221 0.00221 0.00220 0.0021< 0.00213 0.00210.00210.0021 0.00215 0.00214 0.0021# 0.00212 0.00211 0.00211 0.00210 0.0020< 0.00203 0.00200.0020 0.00204 0.0020# 0.00202 0.00201 0.00200 0.001<< 0.001<3 0.001< 0.001<5 0.001<4 0.001<2 0.001<1 0.001<0 0.00133

0.00232 0.00232 0.00231 0.00231 0.00231 0.00231 0.00231 0.00231 0.00230 0.00230 0.00230 0.00230 0.00230 0.002-< 0.002-< 0.002-< 0.002-< 0.002-3 0.002-3 0.002-3 0.002-3 0.002-3 0.002-0.002-0.002-0.002- 0.002- 0.002- 0.002- 0.002-5 0.002-5 0.002-5 0.002-4 0.002-4 0.002-4

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450.000 444.000 4#3.000 4#2.000 42.000 420.000 414.000 403.000 402.000 #<.000 #<0.000 #34.000 #-3.000 #-2.000 #.000 #0.000 #54.000 #43.000 #42.000 ##.000 ##0.000 #24.000 #13.000 #12.000 #0.000 #00.000 2<4.000 233.000 232.000 2-.000 2-0.000 24.000 253.000 252.000 24.000 240.000 2#4.000 223.000 222.000 21.000 210.000 204.000 1<3.000 1<2.000 13.000 130.000 1-4.000 13.000 12.000 15.000 150.000 144.000 1#3.000 1#2.000 12.000 120.000 114.000 103.000 102.000 <.000 <0.000

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0.00130.00135 0.00134 0.00132 0.00130 0.001-< 0.001-0.001-5 0.001-# 0.001-1 0.001< 0.0010.0015 0.001# 0.0011 0.00153 0.0015 0.0015# 0.00151 0.00143 0.00145 0.0014# 0.00140 0.001#0.001## 0.001#0 0.00120.0012# 0.0011< 0.00115 0.00111 0.00100.00102 0.000<3 0.000<# 0.00033 0.00032 0.000- 0.000-0 0.0004 0.00050.00050 0.00042 0.000#4 0.0002 0.00010.00000.00004 0.00015 0.00020.00040 0.00054 0.000-0 0.0003 0.00105 0.00125 0.00140.001-2 0.00200 0.002#1 0.002-

0.002-# 0.002-# 0.002-# 0.002-2 0.002-2 0.002-1 0.002-1 0.002-1 0.002-0 0.002-0 0.002< 0.002< 0.0023 0.0023 0.0020.0020.002 0.002 0.0025 0.0024 0.0024 0.002# 0.0022 0.0022 0.0021 0.0020 0.0025< 0.00253 0.00250.00250.0025 0.00255 0.0025# 0.00252 0.00251 0.00250 0.0024< 0.00240.0024 0.00244 0.0024# 0.00241 0.002#< 0.002#3 0.002#5 0.002## 0.002#1 0.0022< 0.0022 0.0022# 0.00220 0.00210.0021# 0.0020< 0.00205 0.00200 0.001<5 0.0013< 0.00132 0.001-5 0.001-

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400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000

400.000 400.000 400.000 400.000 400.000 400.000 400.000 400.000

400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0

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RTULANG

?b?h

Pn  * Pno Pa/a kon/i!i tekan ak!ial !entri! Mno = 0 " Pno = 0.30?B 0.35? 78 ?b?h @ %!? y  0.35? 78E

P no =

4311 k 0.1 ?  78 ? b ? h ?10 # = 00 k Pa/a kon/i!i balan7e " = 7b = 00 * 00 @  y ? /1 = ##.00 mm →

netral =

100

→

∆7 = .0000 UNIT

0 0# /i #





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MPa

k

k

k

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0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 #3<.5 #--.3 #4.#50.0 ###.#

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0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

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3--4.<2

0.00

1000 <50 <00 350 300 -50 -00 50 00 550 500

φ.Πν (κΝ)

450 400 #50 #00 250 200 150 100 50 0 0

2

4

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3

10 12 14 1

ANALISIS KOLOM DENG

4000 #300 #00 #400 #200 #000 2300 200 2400 2200

φ.Πν (κΝ)

2000 1300 100 1400 1200 1000 300 00 400 200 0 0

20

40

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30 100 1


M

M

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9

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kmm

kmm

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kmm

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!5

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Pn

Mn

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20<10.440-

41320.33

1#42#-.5

235.0

242-.0

#3113.-2

2144.3

515.3

0.5

b= h=

400 00

"%

D

 78 =  y =

25 400

Tul. "

13 20 22 24 2 23 #0 #2 #4 # #3 40 42 44 4 43 50

Pu

Mu

k

km

112.54

2#.#20

12<.-03

21.#14

124.013

2#.33

32.32<

25.<15

1#.043

2.<<#

11.54<

20.454

114.222

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-2.350

#4.-3

mm mm "4

MPa MPa

φ.Μν (κΝµ)

N DIAGRAM INTERAKSI

Tul. "

b= h=

400 00

mm mm

"%

D

"4

 78 =

25

MPa

 y =

20 140 10 130 200 220 240 20 230 #00 #20 #40 #0 #30 400

φ.Μν (κΝµ)

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R.Mn km 0.00 34.34 <2.-2 100.4103.0< 115.5122.<2 1#0.14 1#-.2# 144.1< 151.02 15-.-2 14.2< 1-0.-# 1--.04 13#.2# 13<.23 1<5.21 201.02 20.< 212.25 21-.222.<3 223.1 2##.21 2#3.15 242.< 24-.53 252.025.44 20.< 24.32 23.34 2-2.-4 2-.52 230.13

400

Pu

Mu

k

km

112.54

2#.#20

12<.-03

21.#14

124.013

2#.33

32.32<

25.<15

1#.043

2.<<#

11.54<

20.454

114.222

#1.#22

-2.350

#4.-3

MPa

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